If your wife uses the electronic babysitters, I think there’s nothing truly effective you can do (especially if you aren’t at home) unless you find an agreement with your wife about time limits for the kids. (Hint: there are scientific recommendations regarding screen time for toddlers and children, if you want to go into this discussion armed with better arguments than “I don’t think that…”.)
Once you have reached this consensus, I would warn against making reading and writing a chore. Taking away something that’s super easily accessible (the electronic devices) and replacing that with something that’s harder and needs more energy (reading and writing exercises) will create an unnecessary uphill battle for you. Motivation must be intrinsic to be sustainable, so the ultimate goal is to make reading and writing something that’s positive, part of everyday life and that makes sense for the child doing it.
The typical approach is to consider your own actions first - do you read for pleasure, are books/magazines/… part of your daily life, do your kids see you reading and are you reading to them? (In the latter is a no, I would certainly start there with the first change!) Same goes for your wife - note that reading isn’t just “good” literature, romance novels, newspapers, magazines, even books on gardening or cooking count. This is occasionally described as “monkey see, monkey do”, meaning that kids will typically copy the behavior they see (natural learning process) over doing what they are told, especially if they are incongruent.
The second lever is purpose - an exercise just for the sake of the exercise is frustrating and hard, honing a skill while doing something that makes sense (“is fun” is also a form of making sense) and creates a desirable output is incredibly more effective. Success after comparatively small steps would be especially important for your kids, coming from being used to the frequent reward triggers built in in computer games.
Compare reading a random story or writing some exercise text to the following (admittedly complex) example of how you can practice the same in a context that gives purpose to the effort:
- Read a simple recipe. (Not just working on the reading per se, but also on comprehension.)
- Write a shopping list (that’s writing with a purpose), then go to the store (reading your own text again, possibly add some basic maths on the side).
- Re-read the recipe steps and execute them (reading comprehension).
- Enjoy the results (the ultimate purpose that’s the best possible reward).
Another factor especially for reading: A book or story that captivates the reader is the key to wanting more and more. Supply the right material and let the book pull the reader in instead of you pushing your children towards it.
And yes, it may well be that your child is tired after just a short time of reading or writing. This is a kind stamina that needs to be built up just like stamina for physical exercise. You don’t have to push him over threshold all the time, that’s frustrating. Be gentle here. (Electronic devices are also tiring, but it’s usually not noticed by the consumers due to frequent rewards to the brain.)
If you want “tangible goals”, don’t prescribe a schedule, instead read together (e.g. switching paragraphs or you start and stop just when it’s exciting…) or talk about the book/story/other material. You can write letters (and that could in this case even be done on a computer as e-mail) to each other while you are away - everything from sharing about your day to exchanging riddles or posing challenges.