it'll be hard, but i think it can be done. You will have to take out a large
amt of loans for the col here and the close to $40k per/yr tuition at any of the law schools you named. depending on the neighborhood, a 2 bdrm apt can cost anywhere from $900 (in a not so great neighborhood) - $1800 (in the better neighborhoods). more than likely, your apt will not have a washer and dryer, so you'll have to factor in how much you'll spend on laundry each week & you'll probably have to pay for utilities.
i spend anywhere from $50 - $75 a week on groceries for me & my son. depending on how much you like to eat, (b/c me & my son like to eat a lot) it should cost you a just little bit more w/small children.
children under 5 don't have to pay for public transportation, so you're good in this area...for now!
there's no doubt it'll be expensive, but if this is where you want to be, you'll be able to do it.