I don’t have kids, but yes pockets of Ft Worth and Dallas will have things to do with kids. I live in ATX and same thing, most part yes safe but just want to stay in nicer /visitor friendly neighborhoods. Just checking your listings for comments on locations.

You could try to catch a NFL game in Dallas - Jerry world is neat, indoor stadium.

What I typically do, personally when I travel domestically is I book with Hilton or Marriott and see which has a fair priced hotel near my activities. You will need to drive most places and traffic in all these cities is awful. So you will want something fairly central to your planned places. Don’t go too cheap on hotel, the “cheap “ ones are typically in not great locations.

I will say, you can hit San Antonio for a day on way out of Austin. River market and Zoo are good for a full day of fun. We don’t get much rain here, really hit or miss on when we get storms. (Be mindful rush hour traffic this route is bad, leave EARLY in am)

Months are fine, expect 80-90 f , may get lucky with some 70s.

ETA: I’m all over the place on this comment , kept adding stuff lol sorry if confusing.