I think there’s a leap here that you’re not explaining or that I’m missing from the text. She sounds attractive and friendly, she’s apparently “available”, but what is prompting you to wonder about a course of action? What’s the trigger? Has she already behaved a certain way towards you that’s making you question if there might be something “there”, like she seems to be extra “nice” to you or whatever? Or are you just wondering in general, “Hey, there’s a person I’m attracted to and I want to see if she’s interested?” There just seems to be a disconnect in what you wrote and I’m not sure what prompted it to begin with.
To answer the question though, you can certainly try any of the things you talked about, or try to setup a meetup between your kids, but somehow include yourself and her in on the plans (go out to a movie together or some event) and see if she’d want to join you all. Personally, I wouldn’t try to force things too far and make it awkward, but if you’re trying to gauge interest, you should try to figure out ways to spend time around her or start finding reasons to text to ask about stuff. You also have the issue that should things progress between you two, do things get awkward between your kids anyways, even if you and her hit it off? It could potentially cause friction for them no matter what happens. Relationships are hard no matter what.
That sounds innocent enough that it could go either way. It could easily have been just an innocent thing to have another adult along to hang out with the kids, women tend to not think anything of inviting somebody out to do something like that and don’t necessarily have an ulterior motive. It could mean more though, but it doesn’t seem like a big enough data point to go off of.