lilajanes people will generally respond to the first post, so you might find it better to start your own thread with your question?
Also, there was a recent thread in the AIBU section called "to consider training as a barrister" or something similar. If you do a search for "barrister" you will probably find it. The responses were also discussing training contracts for solicitor roles. I'm afraid to say the overall response was pretty negative.
IMO there are three main things to bear in mind.
(1) It is a lot, lot easier to get onto law training courses (the GDL, LPC etc) than it is to get an actual training contract. These are hotly competed for and there are many people who do the GDL/LPC (and run up debts doing so) but then cannot find a training contract. For this reason I would not advise anyone to try to become a solicitor unless they have at least a 2:1 from a well respected university, and good A levels.
(2) Being a trainee - and even a junior qualified solicitor - means you are not in control of your hours. You work when someone gives you work. That may be at 6pm just as you were getting ready to leave. In fact even when you are more senior, although you have a bit more control, your hours are dictated by the client - they may need something worked on into the evening or at the weekend.
(3) The hours depend on the kind of firm you want to work for. City or big regional firms will expect 50+ hours a week. Smaller local firms or public sector will, usually, not - but even then they can do, it depends how busy they are. Of course, they also pay less, and are less likely to cover your GDL/LPC costs. As this thread shows, part time options are very limited in the law.
Sorry to be so negative! Personally I would say, if you have a job which you enjoy and which enables you to spend time with your DC, don't let it go!