It said the PI was allowed to film interactions that take place in public. Would a motel room be public and therefore legal? Any other ideas?
No, a motel room is private, however, PI's typically take photos of the two people each entering the hotel, and leaving together, and then let the spouse (and the divorce court) assume the rest.
You could have her appearance superb going in, hair and makeup just so, and then in disarray when she leaves.
I'm sorry, but I don't know many women who wouldn't redo their makeup after having had sex with a someone in their house or at a hotel. Few are quite that blatant, especially with the rampant 'slut shamming' common today.
If the cheating wife were at home there wouldn't be a problem because the PI would have the husband's permission. (Not my idea, seen it in a story.)
Sorry, but the laws (at least in most states, require the permission of both parties, thus recording your daughter's private phone conversations are against the law, as is recording a phone call with your wife if she isn't informed she's being recorded (and that consent is part of the recording, thus requiring you to ask them twice).