Yes, of course i would.
What kind of person thinks a partner would cheat given a chance... If your relationship has deteriorated to this point, why prolong the pain? That point aside, there's no need to be unreasonable...
You shouldn't control your partner, much less dictate the sex of those they want to meet - it reeks of sexism and just plain old insecurity.
Do partners cheat? Unfortunately yes, but you can't change that - it's life, you can however stop being so damn controlling