You are responsible for Kibud Av whether it is your parents or your in-laws. That being said, there are respectful ways to “hear” and respond to what your MIL is criticizing. It doesn’t have to be a battle. Do you see her all the time, does she live near you? If not, you smile, say thank you, and then do what you want in the end. You should however, acknowledge the possibility that what she says might actually be good advice. Just because she is your MIL does not automatically mean she is WRONG. APY made the point correctly. You have no obligation to HEED the advice, but you do have an obligation to repond with derech eretz at all times.
The shoe thing is real. When my kids were little, I told them to put on their shoes again – I’m not dead, yet. When they actually saw me sitting shiva for my parents, they first understood why it meant so much to me that they should not do the actions that are seen in a shiva house.
Gotbeer – too many young couples do NOT discipline their kids when in their parents’ homes for a visit. So if “Bobby” is not happy to see you parenting your children, perhaps she should visit YOU rather than you visit her. In your own home, she cannot tell you how to discipline your children, unless you are being abusive, of course.