My understanding is that the chemotherapy risk is around bodily fluids for a period after the therapy.
This means that toilets need cleaning carefully (and some hospitals suggest disposable gloves for this), washing sheets hot (and not leaving in the laundry basket to be handled by others) and being alert to dangers of saliva, sneezing etc.
The biggest other issue is the handling of drugs. Some countries say to use disposable gloves for this too. I think in the UK we just say "wash hands thoroughly" and don't touch anything till you do.
So although a nuisance, if your mother-in-law has help anyway, even if she's not feeling well after treatment I would think there are plenty of adults to make things safe.
Try not to worry about that aspect of your relationship with your husband's family and concentrate on the way to negotiate the childcare problem.
Personally, if I could afford it, I would want to stay at home with my little one - but everyone is different and I know thus would drive some people mad!
Good luck.