When they start asking for money, that's a major WARNING. If it is a legal and real job offer, you shouldn't have to pay. Maybe you should check if this is even a SEC-registered company. I think you can go to their website (not sure though) or maybe there's a hotline. If it's not, I'm sorry but you better find another way to make money.
If it sounds too good to be true, it probably is. Sorry.
I do commend your efforts to manage career and family at the same time. More power to mommies!!!!