I'm not a psychiatrist, but your daughter is exhibiting one of the classic symptoms of ADD/ADHD; a clear preference for putting short-term interests above everything else, regardless of rewards and punishments intended to dissuade her. I hear your account and I'm immediately reminded of my own childhood, having struggled with much the same thing growing up. I refused to clean my room, the dishes/cat box/laundry were a constant struggle, etc etc etc. But, when I'd gotten it in my head to do something, I was borderline OCD about getting it done well. I STILL have this tendency even decades later, though with age comes maturity (or at least the appearance of it).
Traditional reward/punishment reinforcement is less effective on a child like this, because the child will quickly realize the reward or punishment is not a natural consequence of the action. "I get to go to the park if I clean my room? But I can go to the park with my room a mess; cleaning my room doesn't make a trip to the park possible". They will then become interested in the reward, separately from the work to be done (because they know the work doesn't make the reward possible, so it must be possible now), and the reward itself will distract them from the work. As for punishments, they're unpleasant; an ADD child will thus
look for ANYTHING to take his mind off the impending punishment.
If this is the case, the trick is instead to get them interested in the task itself in some way, and then once they've become focused on it they'll pick it up and carry it through to the end. ADD is, IMHO, mislabeled; ADD children in fact have extremely high abilities to focus and long attention spans, provided that whatever they're focused on interests them. Once it no longer holds their interest, or if it never did in the first place, they will actively look for something else to be interested in. Your task is to harness that focus instead of fighting it, by capturing their interest in what you actually want them to do (and not preoccupying them with something they can look forward to later).
This is easier with some chores than others. Household cleaning tasks like mopping the floor are chores a child like this will more readily pick up; It's something they can focus on, there's an immediate result to their work, and it smells nice (always a plus for girls), so set the bucket and mop in front of them and after a little whinging they'll get into it. Same with vacuuming; there's an instant reward of clean fluffy carpet and no more cat hair on the couch cushions. Cleaning rooms is harder to get them into usually because they let it go so long, but also because the scope of the work seems insurmountable and any initial effort they put into it doesn't seem to be making a dent. Dishes are similar; there's often an additional downside that some pots take some hard scrubbing, and some meals just stick to plates worse than others ("She used THAT pot to make dinner? Ugh, I'll NEVER get that clean again", or "Fondue? Ugh, that cheese sauce is like rubber cement"). Offer to help. Many hands make light work, and when the child sees the work progressing they get stuck into it more easily. Offer to mow the lawn in shifts, three laps at a time; that allows them to take a step back and see the impact they're having. Offer to help fold the laundry that the kids run through the washer. In addition to reducing the seemingly-insurmountable task you've presented them with, you also get to monitor the quality of their work ("Oops, this dish still has a tomato seed stuck on it, you'll have to get that scraped off and run it again").
Another thing to keep in mind is that if a job is distasteful enough for you to want to delegate it, there's probably something to be said for trying to make that job less distasteful in general. Contrary to the "Calvin & Hobbes" dad's mentality of "it builds character", the reality couldn't be further from the truth; every time that difficult or disgusting chore has to be done it only further reinforces their hatred of whatever is difficult about the chore, and of the chore in general (and Calvin realized pretty quickly that every time he "built character" by doing it the hard way, Dad saved time and/or money). If you don't want to clean a smelly, bacteria-ridden cat box, they probably will have the same problems with it that you do. Perhaps it's time to invest in a self-scooping box, reducing the maintenance to emptying the waste bin, topping off litter and sweeping up stray granules. If a child sees cleaning their room as an insurmountable task, they might have a point; they may have accumulated so many toys and clothes that when all of it gets bulldozed out of the rest of the house into their room for them to deal with, there simply isn't enough storage space to accomodate it all. A second look at the situation may be called for; you can increase storage space pretty cheaply with baskets on shelves, and/or you may ask your kid to rummage through the pile and make a snap decision to "keep" or "donate" each item they own. If a certain pot or cookie sheet or basting brush just never seems to come clean no matter how hard you scrub, your kids aren't going to have any more success; maybe you should consider retiring that dish or cooking utensil. Look for clothes with easier care instructions so you don't have to be as picky about water temperature and like colors (and if there's anything that's real important to you, wash it yourself). And maybe, just maybe, Grandma's recipe for aged oxblood haggis with Swiss cheese sauce should accidentally be dropped on a lit burner, so nobody has to deal with cleaning up the pot it was cooked in ever again.
Try making the job look smaller. A child could look at a room strewn with dirty clothes, toys and books and think it impossible. So, consolidate the mess. Bring in two boxes, a laundry basket, and a trash bag, and have them start in one corner of the room and make a snap decision about each thing in it. Clothing? Laundry basket. Book? First box. Toy? Second box. Trash? Bag it. When they're done with that, you take the laundry basket and the trash bag away; that's up to half of what they had laying around, gone. Books are easy to put away; that's up to three fourths of the mess taken care of in about 5 minutes. The last box is toys. Tackle the big stuff first; large self-contained toys without a lot of small parts are easy to grab and put in their proper place. Then you organize what's left, putting small parts with larger toys they belong to. By this time you can probably downsize the original box-o'-toys to something smaller, and the child is sitting on the edge of her bed in a pretty clean room organizing the last little bits. The only thing you have to keep an eye out for is the child beginning to play with the toys they're supposed to be putting away in this last bit. A little bit of play as the toy goes from the box to its proper storage is fine, but if they've fooled around with a toy for a couple of minutes you can suggest they come back to it later.
Lastly, instead of assigning one chore to each family member, encompassing an entire family's detritus in that area of home maintenance, have each family member handle their own portion of the chores to which everyone contributes input. When you get up from the table, take your plate, silverware and glass to the sink, rinse them off and put them in the dishwasher. Everyone sorts, folds and puts away their own laundry. Not all chores can be divided this way (you can't really divide up a cat box), but for the ones that can, you create a sense of individual responsibility for cleaning up one's own messes without making them responsible for everyone else's as well. You also get everyone in the family involved in the chore at the same time, instead of one kid facing the cleanup while everyone else heads off to relax or have fun.
The hard part of all of this will be the last 10-20% of any job that needs to be done. Once you've got them interested they'll make a big push at it, then at some point they'll look around, see the results of their work so far and how much of an improvement they've made, call it "good enough" and lose interest. Even adults have problems with this; they'll have put their effort in, made a huge dent, but then be stuck with the last little details that seemingly don't matter until you look at the job with a microscope, and they'll call it "good enough" and move on. This is classic 80/20; 80% of the effort goes into 20% of the finished product and vice-versa, and many people, of all ages, simply don't have that kind of patience. Unfortunately, I honestly don't have a good answer for holding a child's interest until the job is completely finished, because it's bigger than ADD; it is, as I said, human nature for a large chunk of the population.
TL;DR:
- Many kids, especially kids identified as ADD/ADHD, will not respond to a typical reward/punishment disciplinary model. The child will be able to separate a reward or punishment that isn't a direct effect of the job, and so the reward and/or punishment will actually distract them from the task and have the opposite effect than desired.
- The trick in these cases is to interest them in the task itself; once they're interested, they will stay focused for the majority of the work.
- Your strategy will differ based on the type of work you want them to do, but generally you want to either avoid or push past the initial lack of interest:
- For jobs where a little effort has visible results, just get them started on the job however you can, and the results their effort brings will draw and hold their interest.
- Try sharing the load, in various ways; make each member of the family individually responsible for the messes they create like dishes and laundry, and offer to share the work of jobs that just have to happen like lawn mowing.
- Small chunks help. Get them to mow one contained area of the yard; that area is then "done" and they can be proud of that and more willing to move on to other parts. This can be easily combined with sharing the load; by dividing the work, the part the child has to do is smaller and easier to manage.
- For jobs that can take a lot of effort with no visible result, structure the job to get some up-front results. A room can look a lot cleaner very quickly with an initial round of quick sorting into boxes or baskets according to the type of detritus.
- For distasteful jobs, make them less so; if you would rather delegate the task than do it yourself, ask why, and see if there is a feasible way to reduce that displeasure.
- In some cases you may actually be asking the impossible without realizing it. Take a step back and look at why the child is dragging their feet; they may know something about the job that you don't.
- Praise helps. Praise for doing the work is a direct cause-effect relationship, unlike material or "enrichment" rewards. Praise them for hopping to it, praise them for what they've done so far, praise them for completing the job.
- Demonstrating fairness and consistency helps. If Dad doesn't want to mow the lawn (his assigned chore) in a given week, that may be his prerogative, but it's easy for a child to see this and draw the same conclusion about their own assigned chores. If a chore goes undone by the person whose responsibility it is, they should be able to be called on it by any other family member, parents included.
- Unless your child is borderline OCD and really sticks with a job, at some point during the last 20% of the work they will be prone to losing interest. While all of the above helps to reduce this in an ADD child, this behavior goes beyond ADD to basic human nature; at some point a person will call it "good enough" and want to move on.