Here a sincere piece of advise for you. Human in general (and husbands/wife in particular) do not like to listen words “drama” “dramay baz” “acting” “fake” “making big fuss” etc for their parents (specially mother) from SO. Even if you are right, your choice of words is not. Words used in conversation/discussion are as important as the context its-self.
Secondly, if your MIL is feeling (rightly or wrongly) that your husband does not care about her, its your husband’s DUTY to make her feel better/secure just like its his duty to make you feel secure.
and Finally, he can say things to you that he can not say to his mom because dynamics of both relationships are different. I am sure you can say things to him that you can say to your father. Cant you?