People don’t go to sperm donors for medical emergency for their children. It’s just not happening. That’s baloney. What do people do with adopted children? Or people who used anonymous sperm donors? Do they not get their children medical help? That’s crazy talk. Your wife is either ignorant or thinks you are, so she feeds you stories

This guy isn’t a sperm donor. Your wife is in a relationship with a man, maybe just emotional connection and maybe more. Also if she wants this man to be involved in child’s life, you need to see a lawyer. He can sue for parental rights at any point.