It may be what they think is an easy operation, but it has to be stressful. In your boat I would have insisted on private time with your daughter before that surgery, and let the consequences with your wife be what they may.

Father-daughter is a permanent relationship. You should not try to eliminate it because your wife objects. The value of that relationship should be beyond question. In fact if I was in a relationship where I was forced by my wife to make a choice between my kid and my wife, I'd be inclined to choose my kid. Two reasons. The first is that the kid is a permanent relationship and I strongly object to anyone else trying to get rid of those. The second is that whenever ANYONE in my life tries to make me choose between them and someone else, the person forcing the issue loses. That is one game I have no patience with.

Cheers,
Ben