I totally get the "I will do that myself but no one else is allowed to" philosophy.

It is a deliberate choice to allow people to have influence in your child's life. I wouldn't let just anyone bath her or take her to the toilet or do other things that I think only a parent should do either, because:
a) my DD might not feel comfortable with that;
b) it might send her the wrong message about what other people are allowed to do with her; and
c) they might not respect her limits and understand her behaviour the way that I do.

It is not up to my DD to evaluate whether someone is trustworthy in certain things (like discipline) or not. It is up to ME. I would actually strongly disagree with my mother or MIL using time out with my DD as well, since I'm not confident that they would view the situation the same way as I would. I would prefer they speak with me before taking any disciplinary action.