But not talk about where the behavior comes from.  Defining appropriate and inappropriate behavior in your home/presence is always good with kids, and particularly those dealing with alientating family members.  If she says something that's gossip about you, just correct it with the truth, if needed, and move on.  Or simply say that we're not going to engage in gossip.  We also had lots of talks about the difference between privacy and secrets.

Back in the day when HCBM was really alienating hard, we just didn't allow any devices from Mom's in the house.  If they came, we either returned them to her or just turned them off and put them in a safe spot where only we could access them.

I would suggest DH reach out to SD and let her know her tablet will not be allowed, so don't bring it. Take it from her at the door if she does.

Also, yes, call things out - but if you can, in a way that helps her see what's happening (DH should call her out, not you).  Like if she says they gossip about you - "it seems like your mom and SIL want you not to like us" or stuff like that. 

DH only address it if it's 100% known/verifiable. He, and I talk a lot about patience, kindness and giving people the benefit of the doubt and not rushing to judgement (because that's BMs family from what I can tell, they always know best, right?).

The last thing DH really called her out on was her mask wearing in our home at all times unless she was in her room, he pretty much verfied with her that we were the 'dangerous house' (of course we are since BM = good and DH = bad).  He had a very, very long discussion of that with her and the pee on the toilet issue that was also happening.

It needs to be addressed but in more of a "why do you think that?" Kind of way. One time my DH asked my SD14 why she was saying what she was saying, where she got the idea etc... And just kept asking questions and giving contrary examples, the more she spoke the less conviction she had. If he gets angry she won't talk, the key is to be neutral and try to get them to talk themselves out of it. We turned it into a conversation about thinking for yourself.

However you can confront SIL and BM directly. They will deny it but they will at least know you're on to them! 

Absolutely call out the behaviors and let her know it isn't okay to behave that way. I think it sends a message that this behavior is okay if you just let her continue and ignore it. As for the tablet I would let her know it isn't allowed and if she brought it take it away as soon as she walks in.

In most PAS cases, the BM is driving it, but in this case I think SD is in charge and BM is a weak lazy parent who spoils the little schitt.  I'd make sure she is fully aware of who makes the rules in your household, and they will be enforced.  She won't like it and BM will have the choice of supporting your rules or giving up her free babysitter.

You should definitely call out the behavior but be very black and white and matter of fact because usually the lies behind the PAS are based on illiciting emotional responses from the child not fact. The child will still likely argue but you will place a seed if doubt in Thier mind. 

Recently I called out YSD. She told her father she was angry with him because her mother lost custody of her sister. I asked how her father was responsible for her mother losing custody of a child that is not his, he barely knows, and he never met the judge or lawyers who made the decision.

YSD said because he wished it so! 

I said your father has that kind of supernatural power that he can wish things and make them happen.

YSD said yes.

I said if that is true then wouldn't you think your father would use that same  power for something that benefits him, like I don't know, perhaps wishing his own kids didn't hate him?

Crickets from YSD after that.