I don't want my wife's coworker to stay with us for the next forseeable future
Why don't you want them staying with you?
I don't trust him, or my wife's judgement.
While I think you not trusting your wife is a bit problematic, I don't think you're in the wrong here.  You should be allowed to say who you want and don't want staying in your own house!
I agree. I shouldn't feel uncomfortable in my own home.
You live there too. I think you should talk with her and explain your concerns. It could end up badly and paying for a motel might be cheaper in the long run.