If she's anything like our egg-donor, then yeah. She's going to be sweet as molasses to be nosey AND to try to get on your good side.
Looking at it practically (and cynically, yes, but I've been proven right more often than not), you being there means he's now got someone else to pay attention to, who lives with him, and who does have some say over what happens in the house/with the money/etc. She'll want to keep you happy for a while.
Our situation was a bit unique...
My husband, his ex and I all know each other back years ago online. We had the same circle of friends, even though we never met. So when she and I met the first time it was all OMG! HEY!!!!! Wooo! We finally meet! (even though I knew the story - it was still cool to meet).
Then she wanted to be all BFFs because "we were all 'family'". Um. no. I'm not YOUR family, thanks. Then I found out why she wanted to be BFFs.....
Because suddenly this woman who doesn't work had a FULL schedule with meetings and this and that...so suddenly it was "hey do you mind if the kids are over while I (insert whatever here)?" "Do you mind taking them to school on monday morning?" "Do you mind if they stay the week with you while I..."
And obviously I didn't work at the time, so what COULD I say? That I wanted the week to spend time alone with my new husband? That we didn't want to be her glorified baby sitter, when SHE gets benefits for them and we don't see a dime, even though we have them almost half the week? We don't say much at all around the kids but sometimes they do hear our conversation.
And my husband wants them around as much as possible. And that is fine with me, I just ended up getting caught up in not wanting to do it on principle. I eventually settled in right and now I don't care. If I am available and want to do it and she asks, I just say yes. Interestingly enough, it doesn't happen all that much now.
Then again, we barely see/speak to her. And I put her in her place (nicely) when she stepped way out of line with an issue. We set it up so we pick the kids up on Friday afternoons and then Walk the kids to school on Monday mornings. So, if we are lucky, we don't see her AT ALL.