Erm, he's not being a shithead at all. He's seeing some young-ish guy in the house who he knows damn well is fucking his mother. I'm sure that's not the easiest thing to come to terms with for a 13-year-old.
The onus, though, is on the mother to talk to him about things. Ask him to find out what his issues are and explain the situation.
I don't care how difficult it is for him. The OP is a guest of one of his parents, and if he doesn't like it, he can tell his mom he doesn't like it, or he can stuff it. He's got less sense of boundaries than his mom, and he's only going to keep being inappropriately controlling of her sexuality (yes, he is. Making the OP uncomfortable is his way of saying "Mom went and got rid of Dad. Dad is more important than Mom. Mom will pay by never being comfortable having sex again until she makes Dad happy again.") It is not his fucking place to register his opinion. His mother works hard for him already. If she can't have a little sex without him acting like it's his fucking business, then he is in the wrong, not she.