Hi OP, just back from Krakow with similar age DC. Weather wise, August is usually around 22-25 degrees and sunny, you may have a bit of rain here and there and may have an odd hotter day.
Things to see and do:
Wieliczka Salt Mine is great and interesting for kids.
Zamek Krolewski with Dragon’s cave. You can just get tickets for the parts of the castle you want to see and still explore outside, depends what your DC are into.
Park Lema has absolutely amazing physics inspired playground, there is a small fee to get in but well worth it. You can easily spend half a day in there. The rest of the park is free and huge, with playgrounds and so on. Everything very well maintained, clean and safe.
You can take a cruise on the Wisla (Vistula), have a stroll around the Old Town, Kazimierz, although Kazimierz may not be so exciting for kids.
To eat, stick to the side streets coming out from the Old Town and avoid places with ppl dressed in traditional outfits. Mediocre food and really expensive.
Outside of Krakow are some amazing adventure parks: Energolandia, Rabka (which is a very interesting town on its own), water parks in Bialka Tatrzanska, Bukowina and Chocholow. You can take a bus or train to any of these from Krakow. If you have time take a whole day trip to Zakopane or Pieniny.
I would not advise to drive in Krakow or nearby. Public transport is very efficient and easy to navigate and really cheap. A tram/ bus ticket for me and DC cost £1 (includes bus from Krakow to Wieliczka).
Krakow is nowhere near the war zone 🙄there are plenty of Ukrainian refugees, which l very much doubt you would be able to distinguish from native Poles, and signs are in 2 languages but that’s about it.
Krakow is beautiful, very clean, very safe and still relatively cheap but inflation in Poland is growing at much faster rate than in the UK, not sure how good a deal it will be next year.
I have been to Krakow and surrounding areas many times, happy to recommend any other places. There is so much to do there!