You know, after hearing all the other stuff that this set of parents have said to you; I honestly don't know if it is a family that I would work with!
Can the child come for a half day on stats? Seriously? Would YOU go into work that day for a half day? Your boss IS paying you, you know!
I always get really nervous when it is all about the money to mom and dad. I understand that childcare can seem like a big expense. But: a) that is the choice YOU are making by returning to work on a full time basis. Many other families work out other scenarios if they don't want to have that cost. b) When you factor for expenses, etc, we providers DON'T make THAT much money at the end of the day. I don't think I know of any 6-figure earning home daycare providers!
As for them not having any other child care.... tough. That is, again, their issue to deal with. Not yours! Don't let them play on your sympathies to get away with something for nothing. I always tell my parents to have back up care in place. I know it's extreme, but what if I got in a car accident or something? They would have to figure something out, right? May as well do that now. You never know what will happen. And the reality is; I get sick sometimes, and I deserve days off sometimes, and so on. The more pregnant I get, the more I am going to stress to my families that I will work until a certain date, but PLEASE have a backup plan, just in case!!
As for you being so lucky to "stay at home all day".... there is not much we can do to make these kind of people see how not easy some days can be at this career. If they think it's so easy, why aren't they doing it? Sigh. That is why I so value the parents that do take it seriously!!