Legal Question in Family Law in Texas

Adultery is sexual activity with someone other than youru spouse.

It includes homosexual activity.

"Dating" isn't adultery. Having dinner with somebody isn't adultery.

You prove it the same way you prove anything else in Court: either direct evidence (I saw it happen) or circumstantial evidence (I saw them go into the motel room; I saw the lights go out; they didn't come out until the next morning).