This might be something along the lines of ASD, but there is also other possible reasons. For example, some people start to show symptoms of dementia as early as in their fifties and dementia also makes it more difficult to admit that one was wrong or to express emotions or to accept criticism of any kind. My own grandmother acted much in this way (though less severely than your mother-in-law, popsie) and before we found out it was dementia we thought she was just becoming a difficult, bellingerent old woman. In many couples where one partner developes dementia, the other partner subconsciously starts to help out and to mask things towards outsiders which may manifest itself in an aggressive kind of defense.
I'm not saying that your mother-in-law has dementia, but depending on her age and family history that might be as much of an explanation of her behaviour as ASD would.
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