Hi Katy
although not in law, I have a research masters and now am nearly finished my PhD - I did all my study, ie undergrad to masters to PhD as a mature student. I have four children, a dog and a hubby on shift work so I can vouch for saying that it's possible. Although I didn't have a part time job while studying I did teach a lot of tutorials, exam invigilation - you name it I did it! Best advice I can give is that you just need to be prepared to juggle and to be honest as a mother I think guilt is part of the package! Guilt that you're not studying enough, guilt that you're studying too much, guilt that the house is a mess, guilt that your children are not getting enough quality time... However in the end it all gets done. If you are working 3-days a week plus studying plus looking after your family you have to be prepared to work at your studies at odd times. You probably will have to study when your kiddies are in bed or at school or when your husband is out etc. At times you'll resent it but as you say it will be worth it and it sounds like for your particular area, it will certainly be worth it.
Keep all those balls in the air and multi-task (up)