It seems to me like everything is a compromise once you have kids! I feel for you.
Is there any possibility of some flexibility from the new job? Can you be up front with them about DCs?
Even if you worked from home 1 day a week, could you take your lunch at school collection time (with works consent) in order to get to the school gates once a week? Then DH or a childminder taking over so you can continue work. Or do 7 - 3 on that day. I am hoping to negotiate something similar when the time comes.
I work 4 days a week and I am much happier than when I worked 3, overall the family is a happier one.
Why not try it? I appreciate there will be lot involved to get everything organised so you can work full time in London, but what is the worse that can happen? Give it 6 months and if you hate it, leave.
Try also to focus on the positives; more money, using your previous experience, furthering your career, the security of a paycheck, "me time" at lunchtime and on the journey to work.
I imagine your beauty business will still be there, so maybe that could be plan B if plan A above doesn't work. As fatfingers says you can always focus more so on the business.
Good luck