Instead of looking at this as giving up $100, think of the ways you can actually make this a cash flow benefit for your family. I think if you did you will find that it makes sense.
Can you monetize staying at home? Watching other people's kids, even part time, could easily make up the $100 difference, and if you have a stable work schedule that should be easy enough to do. Will you be able to spend more time being thrifty, cooking at home, watching for sales on things you need? Would the new part time job mean you will drive less miles per week (or are you biking/walking)? Can you save money with cloth diapers at home, whereas you needed disposables for daycare?
Lastly, I'm not married and don't know how your relationship works, but will your husband be responsible for less household chores like shopping, food prep, paying bills, etc? I imagine not having to worry about taking care of those things when he gets home could improve his performance at work, and possibly lead to more pay or better promotions.