I'm a TF tutor - not history, but happy to chat about workload in general. I have had parents with young children - mostly mothers, not fathers - do this course as tutees of mine, though none as far as I am aware were single parents.
Things to be aware of:
TF schools have a particular demographic, which may make them challenging places to teach for a variety of reasons. Most have excellent staff and support from leadership, though, which is crucial.
Your timetable will be close to or actually 80%, which is the same as an NQT, you will be teaching from day 1 and will not be supernumerary, which means you will have the responsibilities of a qualified teacher. As an employee of the school you may also be required to do some break/bus duties - you won't be a form tutor, though towards the end of the year you may be attached to a form to learn about it.
You will be required to do two assignments in each of your two years. This includes some training days - usually in the week, occasionally on a Saturday. Your tutor will support you, but it will be extra work across PGCE and NQT years from September to May time in each year, usually with deadlines after Christmas (busy with the kids!) and May-ish (exam season, your own QTS assessment time in your first year).
I have seen many excellent trainees excel in their training and quite frankly, if you can complete the course and succeed, you have every chance of succeeding in a teaching career. Also, I have found my opposite numbers in TF (tutors are employed by universities which work in partnership with TF) to be excellent and TF as an organisation to be hugely supportive of their trainees.
Good luck, what ever you decide 