What was his reaction to you making that comment? I see it being extremely damaging and nothing good coming from that. He’s allowed to have feelings and wants too. Be glad that he said he’d reconsider in a few years. Remember that vasectomies are reversible and have the potential to fail at the same time so you can see how serious he is if he really does his follow up appointments. I think he’s being more than reasonable considering you recently had a second child. Give it time and stop being so dramatic.
Deep breaths. Give it some time. Apologize for the sperm donor comment; that was not ok. Ask him to please holf off on the vasectomy for a bit. Revisit in 12-18 months. While going through the newborn stage is not the time for this conversation. Everyone is emotional. If you still aren't on the same page in a couple of years, see a therapist to work through it. If you did go through the sperm donor thing without his consent, he should divorce you. No one should be forced into a child they don't want, and even if you use a sperm donor, you'd be bringing the baby into his family and expecting him to treat them as his own. Unacceptable.
All I'm hearing is what you want. Granted, he might have been happy to have 3 in the beginning but got a bit of a reality check after two. After all, babysitting someone's kids you give back is different to having your own. Babies are expensive financially, emotionally and time wise. If he has said he would consider this in 3 years, let him know you will hold him to it. The sperm donor comment was harsh. Would you expect him to claim and support this child that he doesn't want, that has none of his genes?