Hi. I qualified in 2008 but left private practice in 2014. My advice (for what it's worth) is to apply for firms that sponsor the LPC. OK, not magic circle because of the brutal working hours, but maybe ones with a strong reputation for family such as Withers, Pennington Manches, Charles Russell Speechleys, Russell Cooke or Mishcons or a West End firm. Yes, the hours won't be great there either and you will probably have to get some good childcare, but I think the hours would be long at a smaller firm too. At the end of the day, it's not a child-friendly profession. However, your advantage is that you have children now so can focus on your career without having to worry about taking a break in the future. I think that with a good degree from a very good uni, you stand a strong chance of getting a training contract, especially with your work experience.
Sorry to CILEX people, but I wouldn't do it if I were you. The pay is atrocious and the training takes a long time. My friend who finished the LPC in 2008 and didn't get a training contract did the cilex route. She has been working for 7 years now, specialising in family law (in a West Country firm) and got her fellowship in 2013. She earns £22k and still lives with her mum as she can't afford to move out. From your academic background, you should be able to follow the traditional route which means faster qualification and much more money.
I did my training at a regional commercial firm and then worked in a London firm post-qualification. During my training contract, my hours were OK (apart from my corporate seat). Would probably be a bit longer in London though but I would frequently leave at 5.30 if not particularly busy. One of my fellow trainees was a mum of 2 kids. She was 31 when she started her training. I think she occasionally had some issues with childcare, but on the whole, the firm supported her.
I had a trainee a few years ago who was late-30's with 2 young kids. She was also able to juggle things and was just super-efficient during working hours (which is more than can be said for a lot of solicitors).
I think you will be fine. Your age won't be a drawback and you have good experience. You could also look at regional firms (in Kent for example) which tend to have a better work/life balance.