I've been on both sides of this issue.

As a SP, my parents are nice to the kids. That's it. My MIL and DH's ex-inlaws are very involved with the skids.

That's what the story was for me growing up also. My stepparents' families were nice to me. I was nice to them. My grandparents were my grandparents. Hopefully BMs family didn't drop out of SDs life?

I say let your SD and your parents work out something they're all happy with and go from there.

My thoughts on that are...

The skids were abandoned by BM and her family. So, now, your family should treat them like "foster kids". You acknowledge them as a part of the family. But not...100% yet.

Basically my Mother treated my foster boys like they were friends kids coming over for the holidays, they each got a gift under the tree and were included in family things, but no one made a special fuss over them. You want to give them NORMAL family memories. And I would stay on that route until...Well as long as they live full time with you.

MY foster kids were treated well, but we did nothing fussy for them. Yes they got to be involved in the dirty santa games and what not like everyone else did. They were not however...say invited to the cookies and milk at 4am with my Papa tradition that has always happened with my family. They DID NOT know about that tradition either so they didnt get unintentionally hurt.

I think my parents have gone overboard with my skids. Last Christmas, they bought them a ton of presents and once we told my parents that me and DH would be having their first grandchild, my mother was telling me that it's ok for the skids to call her and my father their grandparents. I told her no. I told her that they were not their grandparents and it wasn't necessary. SS11 doesn't give a crap about either one of his biological grandparents and I'm not going to have him treat my parents the same way. SD14 clearly prefers her maternal grandmother over DH's mother (even though this woman put SD through a bunch of mental crap when BM was living with her for a while) and she doesn't really talk that much to my parents. My mom said she was just trying to be fair and didn't want the skids to feel bad when my DD is calling them grandmama and granddaddy. I pointed out that DD was going to be calling me mama and the skids don't. I also told her to stop buying them so much stuff. They don't appreciate it (SD even complained about one of her presents) and it's not fair because they are getting gifts from THREE sets of "grandparents" vs my DD will only get gifts from two sets. Once I explained it to her, she understood.

I just expect everyone to be cordial. I think once kids get to a certain age they understand the dynamics. Your SD13 should be old enough to understand who's who and why your mother may pay more attention to your daughter.