Hi OP,
To me the most striking thing in your thread that I would question is that you don't want to sell your flat because you see it as an investment.
If you had said "I don't want to sell my flat because it is beautiful, I am so attached to it and living in this area is my dream" I would totally understand that, but because it is an investment no I don't get it.
Most people choose where they live because it suits them best - especially when they have a family. You could easily give your kids a room each, a garden, a lifestyle with holidays and more of your or their other parents time so they could go to activities they choose, or have playdates. A theoretical "investing" in your London flat seems the worst reason not to do this.
So your flat might be worth 100k more in a few years, or 200k more or a million more but your children won't get a second childhood, and you won't get a second chance to raise them. You and your partner earn very well - you don't need to live a less nice life on the off chance your equity goes up.
If the equity in your flat does go sky high what is the game plan? To sell up and get out of London with cash to buy your kids properties as well as your own mortgage free? But by that time they will have missed the chance to build connections in a new area and probably won't want to leave. Your flat will only ever be worth the cost of a two bed flat if you stay in the area and your kids are unlikely to be able to buy near you - especially if you can't help them.
It sounds to me (when you talk of your hard work and not wanting to take another job that would reduce the pressure but is less pay) that your goal and driving force has been to earn the most possible, and that the high earnings is important to your self esteem. I think personally that a much more sensible goal, especially when you have kids, is the best quality of life possible.
You and your family might, for example, have a much nicer quality of life on half the household income if you had less work hours, less work stress, more time and more spare cash for activities, days out, holidays etc.
It will be much more likely that your kids will be able to buy their own homes near you and their friends one day (if that's what they want to do) if you don't live in London.