Meh, not really.
From this link:
https://www.huffingtonpost.com/deanna-brann-phd/the-mildil-competition-it_b_4461464.html
The main factor in why it’s so different between MILs and DILs is that there’s an undercurrent of competition between the two women — but it’s not what you’re probably thinking. Most of us want to believe that this competition is for the husband/son’s love. That’s not it. The competition is actually for the influence each woman has over this man in the middle.
This is an unspoken competition. Most women will feel some tension around something the other did or said, and then they will find fault with the actions displayed by the other. For example, a DIL may complain that her husband’s mother won’t let go, or a MIL might say that her son’s wife wants to keep him from the rest of his family. Making these statements or having these reactions is really how each woman tries to deal with the covert competition. These statements and/or reactions are the consequence of this undercurrent of competition, not the cause.
I think of it as a scuffle for control of the family culture. Family culture is largely established and maintained by women, so when a man marries, his wife creates the new family's culture. If that culture is at odds with the culture in the husband's family of origin, his mother (who established that family of origin culture) experiences it as a rejection and feels threatened.