I think if the OP is honest enough to describe her own mother as "overbearing" in the OP, then we can assume her husband does have a point.
She also says that things blow up, her mother backs off, but things then blow up again.
That definitely reads to me as if her mother was overly involved in their marriage.
Parents have absolutely no business telling their children how to raise their grandchildren nor sticking their nose into their childrens families.
The OPs mother has caused stress for a while now and has not been firmly enough told to take her overbearing behaviour away.
Neither me nor my husband would ever tolerate an overbearing parent sticking their nose into our family, not for 5 minutes.
I feel very sorry for the OP, but I think she needs to be very honest with herself about this and what her priorities are.
Is her mother more important than her marriage and her children having a happy dad living with them?
None of my friends would have tolerated such interference in their home like this for a minute.
Conversely, could he be using this as an excuse to leave?
Is this the final straw in an otherwise happy marriage?