The fact that the child only acts this way at home says to me it is a learned behavior, not "wired" into him.
It sounds like neither parent is willing to enforce consequences for his behavior. If they don't start teaching the kids that there are consequences for their actions it's only going to get worse. Eventually the world will teach them the lesson.
IMHO, you are not being overly critical. It is wise that you are wondering if this is the right relationship for you. If the father is unwilling to change how he parents the child's behavior is not going to change. Why should it? He gets what he wants now, why change? There's a good chance his behavior will escalate as he gets older. If you don't think you can live with the behavior it might be time to bail out. The man may be wonderful in other ways, but his kids are always going to come first.