It may be possible, but potentially much more of a hassle (and hence much more stress) than it's actually worth. From what I've heard from every law student I know, 1L is a full-time job. I know people who do it in a regular 40 hour work week, but none who do it in less. And law school schedules are pretty full - I'll have classes every day, sometimes from 9am until 4, with an hour break here or there - certainly not enough time to run home and let the other parent go.
Many law schools will allow you to take out loans not only for tuition+living expenses, but for day care. Your child will be over 2 at the time - the age than many children begin to benefit from more socializing experiences. What about part-time care, so your spouse could take his classes part-time in the am or afternoon, without impinging upon your law school schedule?
I've had five kids, and for much of the last 12 years have been a SAHM (with some periods of seasonal, i.e., bi-annual campaign) work thrown in. My spouse now works mostly from home, but has periods of international travel for 1-2 weeks. He already knows that this is my time to pursue my career, and it's his responsibility to figure out child care when he has to travel. It's really hard for both people in a partnership to pursue their own goals at the same time without there being major compromises - and I honestly don't think it should always be the woman who does the compromising, though it often seems like that's the case.