Taking care of other kids while they are at work is one of the most successful ways for a mom to stay at home with her own kids. However, government regulations for day center, even in the home has grown very rigorous and sometimes involves costly renovations. Savvy home daycare owners apply for government grants to help pay for the costs.
Department of Children and Family Services (DFFS) offer assistance for low income families to pay for daycare while they are working. DFFS offers several grands and programs that help home daycare's get set up to take the kids in their low income program. The downside is that you will have to wait on the government to pay you every month. The upside is that you get paid.
Many county or city governments have special funding initiatives for child care through community based programs. One particular program that comes to mind is early head start. Many times the program director will help the individual get approved by finding private sources funds. Check with family assistant programs and welfare offices for more direction in where to find such organizations in your community. as may local early childhood professional organizations or child care resource and referral agencies.
The Department of Economic Development offers small start up grants for business that are ran by women. While this may exclude dad who want to open up a daycare, this is the best way for a mom to get help with the cost of a home daycare.