I think that you need to keep doing what you are doing and distance yourself from her entirely. If the face you get isn't the friend, then she's a business partner/coworker only. Keep it short. Keep it professional. Keep it distant. Don't invite any more chummy behavior. Make the boundary that no, she can't come to the pool, drop off her kids, etc. Don't chat about the pool or park or whatever with her. Be vague about plans and activities and small talk. I think sometimes in the effort to be nice we get into the "feedback loop" of giving too much info. Sometimes it's better to say, "No" than to try to soften the blow.
Now, it does get tricky if you have a kid who wants to be friends with her kid, but sometimes the way we handled that is that our child could only do the things we were willing to be accountable for - ONE child, the child's friend. No siblings. A pick up and drop off defined by us so that we weren't stuck for hours with a child. Even now we have one girl whose parents are always late and if we need to be somewhere she can only come with if we're able to drop her off when we need her to go. We've flat-out told our kids that their friends' parents' lateness is a problem which is why it has to be this way.
If you think she might try to take advantage of the pool, you can tell the pool that she's been trying to take advantage of your membership and you are not inviting her.
I try to think of it this way - is it any more 'rude' of you to say no than it is for her to try to take advantage all the time? No. She's being rude to YOU. So don't do her any favors.