To the mother with the crazy MIL ( and I am 99% on your side):
If you leave your kids at your MIL's house, then her rules apply. If you don't like the rules, then don't take them to the MIL's house. I think the crazy MIL was totally out of line here, and owes you AND the kids an apology, but she doesn't need your permission to discipline the children (within reason) while they are her responsibility. You chose to send them over there; you submitted to her authority. I'm not saying she can beat or otherwise abuse them, but yes, she's within her rights to put them in timeout.
Now, since you now know that she cannot be trusted to treat your kids the way you want them to be treated, don't send them over there.
The fact that she called you a "stupid girl" is a pretty clear sign that you and your husband need to be a united front and tell her that she either treats you with respect or she has no relationship with you, your husband, or her grandchildren. She sounds like a bully and you've got to squash that garbage, because it's not going to go away. Your kids deserve better than to be 3- and 6 -year old pawns in an emotionally-charged power struggle.