To those asking for a source, I believe I gave one. Kiruv l’arayyos. This is D’oraysa. You are free to dispute that mixed swimming = kiruv l’arayyos, as I do not know of an explicit source in Halacha, but this is the issur involved (if you accept that it is assur in and of itself).
I brought the example of sleeping in the same bed because that is an example of kiruv l’arayyos used in Shulchan Aruch. FTR, the SA says explicitly “afilu hu b’vigdo v’hi b’vigda”, i.e. even if both parties are fully dressed the issur applies. That is an exact quote.
Regarding a father/daughter, the SA does not specify an age limit but rather a sign of the time (when the father would be embarrassed to undress before her, it becomes a problem, until that point it is not).