Argis isn't going to do anything. It would violate his oath as housecarl. And why would he want to ruin a sweet gig like that, just sitting around 24/7 and having all the bread he can eat?
Kinda surprised the housecarls don't get fat; all mine seem to do is sit around eating bread. You'd think they could at least clean up the place once in awhile...
But yeah, the OP is totally not giving Argis enough credit here. But if he's truly that jealous, he can just move his wife to one of the houses with a female housecarl, anyway.