In my experience, getting a toddler ready for bed starts the minute they wake up from their nap. They have so much energy, it's up to you to make sure it gets burned up at the right pace to ensure there isn't a surplus at the end of the day. Unfortunately, unlike a surplus of wheat, a toddlers energy cannot be shared (in fact it sort of has an inverse relationship with a parent's energy level doesn't it?) So, here are my suggestions to help you keep your LO's output under control:
The first thing I'd look at is her nap time. It's either at the wrong time or it's too long. My kids never did well to sleep past 3 pm, or for more than 2 hours. Their bedtime starts at 7 and they are usually out by 8, 8:30 at the latest. Not napping is not a good idea at this age, except, on a day she sleeps very late, you might decide to skip a nap in order to ensure she's quite tired which will aid your effort to implement your new bedtime (not new routine, just a new earlier time).
Next, I'd look at her afternoon, starting with her activity level. Is she getting enough exercise in the afternoon? My kids swim in the morning (which tuckers them out for a nap VERY effectively) and play outside most of the afternoon-in all but the worst weather (bitter cold, lightning, downpours, or sweltering heat, all of which are par for the course here in New England). Or, if stuck indoors they will do some dancing, some tumbling, or some wrestling (I have boys). Anyway, the point is, kids need to move and be physical, (and not just because it makes them tired.) The key to this is that it should occur well before bedtime. I disagree entirely with the advice given above to engage in physical activity just before bed. It gets the heart rate up and that is exactly the opposite of what state your child should be in before bed! Quiet time should start after dinner, with few exceptions (birthday parties, holidays, etc).
The other aspect of the afternoon that I'd look at is how much mental stimulation she's getting. If she's watching tv, I'd limit it to a half hour. Instead, puzzles, coloring, blocks, duplos, play-doh, dolls, or housework (really!) all get the mind going, which wards off boredom- another bedtime killer. If kids don't play during the day, they'll play games with you at bedtime (how many glasses of milk can I get out of mommy? Let's count!) Doing these activities after some physical activity ensures they won't wiggle right out of their chair, and helps them wind down so they can be civilized at dinner.
At this point, if your naps and afternoons are just like I described, the next places you can implement change is to dinner and bedtime itself. I'm not going to get into diet too much, since I'm not a nutritionist, and since most toddlers I know are fussy eaters anyway, but I will mention that sugars and too many quick burn carbs will give your kid energy she doesn't need at the end of the day. I've become that villainous mom who doesn't let her kids have juice at dinner. It's milk or water. End of story.
Depending on what time you have dinner, you may go right into your bedtime routine or you may have a few hours. If you have a few hours, try to:
• keep the energy level mellow by enjoying some reading, soft music, and light housework (include your daughter with clearing dishes, laundry, tidying)
•avoid tv, computers, and bright lights
From your post, I'd say that your actual bedtime may need adjustment. If your daughter is showing signs of sleepiness at 7, you should aim to have her in bed by then, not just starting her routine. Kids quickly go into overtired mode, especially if they have energy reserved. You want to avoid that at all costs! So, whether or not you are already doing all of the stuff I mentioned, the only thing you may need to do is move the routine start time to 6 pm so she's settled in bed by the time she's usually tired. Otherwise, go ahead and try any/all of the other suggested changes to her activity level or nap schedule. They should intensify her tiredness to the point where she falls asleep much quicker, and ensure there are no reserves to available reanimate her if a window of opportunity exists.
As for the bedtime routine itself, which you seem to already have established, I'd strongly suggest adding a bath. A warm bath works to calm kids by raising their body temperature and then dropping it (as the water cools, and then when they get out). This helps trigger sleep. A shower can work too if it's all you've got but a bath works better. A bath with calming aromatherapy (such as lavender) bubble bath works even better! This will extend your routine a bit, but should shorten the overall time from when you start to when she actually falls asleep.
Finally, I'd stop allowing my toddler to hold me hostage at night. If you're starting her routine at 7, and she's still demanding drinks from you at 10, that means she's dominating (at most), or at least disturbing, 3 hours of your evening. As long as you are giving her attention, she'll continue to take it. After you tuck her in and say good night, leave. And stay out. Let her cry. At 2, she's got to learn to settle herself. If she gets out of bed, put her back in and that's it. I won't elaborate bc there are other good answers on parenting se that go over this, but basically she'll eventually learn to just go to sleep because there's nothing else to do. (Staying up is boring if nobody's gonna play games or keep company!) some nights she might stay up for hours, but at least she'll know enough to stay quiet. If she's sufficiently worn out though, these nights should eventually be the exception and are nothing to worry about. You just can't make them them sleep sometimes. We all have those days, right?
To sum up:
1) keep nap short; time it right
2) get busy in the afternoon
; first physically, then mentally. Definitely both.
3) avoid sugars, especially late in the day.
4) promote quiet time after dinner to encourage winding down.
5) trigger sleep naturally with a bath and aromatherapy.
6) tweak your timing based on cues
7) be patient and persistent.
I'm confident you will be successful on your quest for a sleepy toddler before 10. You're on a path well trodden by weary, frustrated, and impatient parents. I hope my breadcrumbs hasten your journey, but if not, you'll find your own way. Good luck!