My house rule is-any kids in my home are expected to follow my rules, parents should be warned in advance, if your kids aren't trained to follow my rules, that is YOUR problem-they will not be given leeway.
That doesn't even mean LIVING in my home. Visitors have the same rules. Parents are responsible for finding out my rules and expectations for children in my home AND ensuring that their children follow them or consequences will be handed out. Period.
I don't babysit ANYONE's children who don't give me full authority to act as I see fit in regards to ANY situation that arises with the child while in my care. Period.
I do babysit.
In fact, there are two girls (now ages 12, 9) who I have watched frequently since they were babies. One is allergic to peanuts. She is also bipolar and ADD. She struggles in MANY atmosphere's because of not understanding rules (which are different than the ones she has at home), attention span and issues with anger management.
However, she is in my home regularly and I have NO problems with her. Primarily because, I educated myself about her needs and her realities. It's UNREASONABLE to expect her to not get distracted when being spoken to, in a room with other things going on. SO, I ask her to come talk to me alone if I need her to pay attention to something I am going to say. It is unreasonable to expect her to manage her emotions the way a "normal" child her age would. So I don't allow her into scenarios with other children that are beyond what SHE IS CAPABLE of managing-regardless of "age appropriate norms".
I also watch my grandson. He's 2. He is expected to follow my rules-which do differ somewhat from his home. Again-not difficult for him to do-with age appropriate reminders such as "LP, we do not do xyz in Grammy's house" and "LP, at Grammy's house balls are yard toys, not in the house toys".
If you can't mesh with your partners expectations or vice versa for the care of their child-don't watch their child. It's better for the child, better for you and better for them as well.
"Love As Thou Wilt"