To each his own, but, Hungarians would frown upon children not enjoying the baths of Budapest.
It's been a while since I frequented the Hungarian capital's thermal baths, but, gender segregation is less a thing these days, though it might be possible that in some baths, on some evenings, children might be barred from entering.
All the thermal baths in Budapest are pretty awesome, both for adults and kids. I suppose the only thing you have to really keep in mind is that these are not pools. They are thermal baths. Several of the baths include a more regular swimming pool (like the Szechenyi and Gellert, but both their regular pools are outside), but the focus tends to be more on the medicinal side.