I don't think I have read a unanimous thread on GN before! Even without the dog, I don't think it is unreasonable for you to say that you don't want her to have your baby overnight. I know that grandparents sometimes take it personally because it seems like a lack of trust and they feel that they managed to bring their children up without mishap but that isn't the point. I'm afraid that if your MIL was trying to bully me, I would dig my heals in even more.
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