relaxation, it is NOT your place to teach your mother-in-law how to behave. Lets get that on the table to begin with. However, it is your place to teach your children how to behave and to tell them that YOU are their parents and you decide what they are allowed to do and what they are not allowed to do. YOU can tell them that if you take them for a visit to their grandparents and they don’t follow your rules and don’t behave appropriately, YOU will cut the visit short and take them home.
You can decline going for sleepovers and tell your mother-in-law or have your wife tell her mother that it is getting too difficult to pack and shlep and you prefer to visit on sundays. You can invite them to your home for a Shabbos so they don’t feel like you are ignoring them.
As far as her relationship with her own friends and guests, that is not your problem or issue. She will have to learn on her own, or her friends will have to tell her that she needs to calm down or back off. YOU are NOT her child. YOU are her in-law child and there is such a thing as crossing the line. Be very careful where you tread. She might forgive her children for confronting her because they ARE her children and a mother will forgive her children no matter what. But you are her daughter’s husband and if she feels that you hurt her or humiliated her in any way, she might never forget or forgive.