I would keep Gunther away from the family, personally. (But I am not the type who usually dabbles in affairs, it would certainly bring more drama to your story, though, if that's what you want!) But it sounds like you don't want the affair. Since you're letting whims dictate your play and if Eliza got a whim to talk to or chat with Gunther, then I'd invite him over and let things to take their course, but since she hasn't had any romantic whims for him, I'd play the way you would prefer (monogamous), until the whim dictates otherwise?
Unless you would prefer to let autonomy dictate your play as well, in which case, you should let it happen.
