Why are the most ornery ones the ones we love the most?
Couple of thoughts -
If he's not too high up you may be able to catch him with a net (you can get one at a sporting goods store, a good size fishing net will cost you $10 -$20), or even net him on the ground if you can get close at all.
If you have to wrangle him every day or night, you should pen him, separate from almost all the other chickens who roam (let him have a few hens for company) in a pen/tractor with a cover so he can't get out. Otherwise, he's going to get loose and do what he wants and you will have to face hunting him down to feed him every day/night, and the problems will simply continue. It's the best solution for him (he will get steady food, regular beak trimming when he needs it, access to hens, and protection from predators, which he doesn't get in the tree), for your family (who do not really want to deal with him either because they are afraid or they don't care for him), and for you (no more trying to coax your spouse into chasing the rooster down & any arguments that may ensure regarding said rooster, no more trying to find him when he's in need of a beak trim). Also, if he is in a pen, perhaps your kids can interact with him & not be so scared of him. Maybe they will even come to see in him the things that you like so much.
Do something about that allergy if you can! You want to be able to enjoy having your chickens, and not being able to be near them is definitely going to take some of the fun out of that (my husband suffered with terrible allergies and asthma that required two years of shots and now is controlled with medication - it can be done). From your post it's clear that you are the person who will have to provide the chicken care, since your children fear the rooster and your husband doesn't want to get involved. If that is the case, then you should do what you can to treat those allergies so that you can provide that care, and get the enjoyment out of your chickens.
And if you can't change your situation, it's likely that you probably won't have to watch your rooster starve to death. The life expectancy of chickens that roost outside in trees is not very long. Raccoons and owls (usually barred or horned) are not at all inconvenienced by a chicken roosting in a tree. Rather than seeing him starve, it would be far more likely he'd just "disappear" one evening.