When we were kids - up until about 8 or 9 years old - we always wore lifejackets. We were good swimmers but the water is very cold. We whined, begged and tried to take them off but every time we did, the boat turned around and my father tied up for the day. No arguing, no discussion - sailing was over.
On the rare occasions that I have children aboard, same rule applies. As far as the down below versus in the cockpit issue goes - if the wind is up I'd sooner have the child up where I could see them with a lifeline firmly attached.
That said - sailing is not a democratic exercise and when you leave the dock the skipper's word is law. SO - you need to decide that you and the offspring are going sailing in winds up to say 15 knots or 20 or whatever your comfort level is. Just do it nicely, don't argue, don't be aggressive about it. Just let the other half know that you think it's better to stay home if you're not enjoying yourself. Things will probably change...