The most interesting twist to this story (and it highlights a few important things) … is the fact he could not get a vasectomy because she said no, and the fact she stopped it.
She wanted a second child but couldn’t be honest with you.
The therapist is providing good suggestions, and I would suggest you schedule a vasectomy immediately if you are going to have sexual intercourse with her and go to the doctor and demand you have one and if he says no. Then ask him to refer another doctor and if that doesn’t work … go to planned parenthood. If you feel you are going to be personally effected, then disappear for a few days while you recover from the surgery in a hotel room.
You shouldn’t have to do that (and she should be forced to sign the doctor’s note if required), but frankly you sexual rights have been impacted.