He can't force her to leave, no. But he can MOST DEFINITELY tell her she is not welcome, and that he WANTS her out, and he is in no way required to make her feel welcome there or make things easy on her.
Go dark. Cordial but Curt. No unnecessary communication.
Do not touch her in any way. If she touches or hits you, mAke sure you are recording stuff.
Just because you can't legally "force" her to leave doesn't mean you can't conduct yoursrlf in a completely legal manner that will achieve the same result. It's about commanding respect. At any rate, in bb's case, it sounds like she's already gotten the message.
And, fwiw, if there are children because involved I think there may very well be some jurisdictions that have provision for requiring an adulterous spouse to leave. For specifics, though, you should really consult a lawyer (I am one, but only licensed in DC and VA (and occasionally pro hac vice in Indiana)
H53/W51, R-ing 4/'18
"Do not arouse or awaken love until it so desires"-Sg.of Sg 2:7
"So oftentimes it happens,that we live our lives in chains, & we never even know we have the key"-Eagles III 1:3