I think your MIL is from the old school of thought were daughter in law has to maintain distance from the men of the house, and same for the daughters of the house too.
if she is so uncomfortable with your relationship with your FIL and if your FIL has not clarified it out himself, and not even your hubby, I don't think it's worth it. Also, it is not just you but she has a problem with the granddaughter getting close to the grandfather as well. I guess back off for some time. If your FIL does not take a stand, you should avoid getting into something like this.
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