You don't say if these houses are owned or rented. If she is renting perhaps talking with her landlord might help. If she has a husband or boyfriend living with her, it might help for a husband or boyfriend to talk with him. Men do seem better able to resolve issues at times. There are usually less feelings involved.
I would also check with local city ordinances to see if there is a law against leaving a pool accessible to neighbors in such a situation with water in it
I had a wading pool in my yard for my grandchildren and we didn't leave the water in it for longer than a day or two because the water would get dirty with grass clippings. A couple of times I left the water in it for a week and the bottom and sides got slimy with algae. Eventually we just stopped using the pool because it required too much work. You might just wait and see if she does keep it out and full for any length of time.
There is a web site and a book entitled Non-violent Communication that has been mentioned often on this site. I think this would give you ideas on how to approach her. She sounds like someone who is quick to take offense and who doesn't want anyone telling her what to do. I've dealt often with this sort and have found it helps to not ever tell them directly what you want. Educating works better.
You'll have to wait awhile now that she's "up in arms" but you might try mentioning having read about how small children drown in a bucket of water and how concerned you are for how she'd feel if that were to happen in her pool. Pad it with lots of approving statements such as I think it's a great idea to have a wading pool for your daughter. And towards the end, if she's still listening suggest that you'll help her find a way to both have the pool and protect the little kids. The most obvious way being that she empties it when it's not being used. Yes, it would be full for a day but probably not every day which would be a compromise.
With her one definitely wants to start out with a statement about how she has the right to do whatever she wants in her yard. Tell her you don't want to tell her what to do. Be very careful to make comments that give her the sense that she has the power. Not an easy thing to do when you've already gone rounds with her.
As a last resort and only if she leaves the pool full and not used, I'd call the police desk and ask to speak with a supervisor in your neighborhood. Perhaps an officer could come out and talk with her about the dangers. When I was working, we used a form of law enforcement called neighborhood policing and we would do that sort of thing from time to time. I was most willing to do that when the caller was calm and reasonable and not expressing anger. Technically, the police cannot force her to do anything, most likely and I did not like to get in the middle of a neighborhood squabble when there was nothing I could actually do.
For neighborhood squabbles our city/county has a Neighborhood Mediation Office. Perhaps your city has one too and you could try that. Ours is listed in the phone book business alphabetical section. Or it might be listed on the government pages. The police department would also know how to reach them.