Hmmmmm... I'm not a parent, but I do have some friends in med school that are. My friends have MADE it work -- most of them work like CRAZY during the week (4+ hours of studying per day in addition to class) in order to take weekends off to spend with their children. All of them have a spouse that works in a nonmedical field, and that seems to be immensely helpful. It's not impossible!
As far as your financial situation, if you have absolutely NO money now (or are paying for undergrad by yourself), your wealth won't change much during med school. You'll be taking out heavy-duty loans to cover both your education and your family's upbringing. If you don't mind being in debt, it may be possible.
One thing that is certain -- I would NOT recommend telling your interviewers about your family life. It's possible you will be discriminated against because of your situation. Heck, I told an interviewer that I might want to TEACH for 10-15 hours per week and she snapped at me, telling me it might not be a good idea.
Good luck!
