Hi missy, I haven't studied with los, but from a lecturer's point of view, I would definitely recommend doing the part-time course. Being 30 isn't a problem at all (some of my best students were in their 40s and 50s - really odd when I was only in my mid-twenties at the time and they new *lot* more about Thatcherism than I did! :lol

but it will be a problem if you end up struggling to make deadlines. Lecturers and departments will be pretty sympathetic to any (inevitable) childcare crises, but a lot more so if you go in having given yourself as much time and space as possible to do a good job of studying.
It is definitely possible to study with children. Lots of postgraduates have kids and, as I say, universities are usually pretty sympathetic to parent students if they are committed. It may be worth investigating whether the university you plan to apply to has a creche. If so, it should be open to students as well as faculty and will make your life a lot easier as it will be able to work with student schedules.
As for when you apply, it may be worth doing it now, before the funding report is out (later this year) as tuition fees may go up. Just another thought to add to the mix (sorry!).
Best of luck with it. And for the move as well!