For the ice pack situation, maybe you could freeze water in a plastic bottle (from water, pop, juice, etc). Those are sturdier and might last longer, and if he does bite through them you could just throw them away. (You could also use yoghurt cups, sour cream containers, etc-- any kind of plastic "trash" that can hold water once.)
Make sure he has a stick or something similar to chew on, because rabbits do need to chew on something to wear their teeth down. But if he's already got a stick, then he probably just likes the taste or feel of the ice pack.
You could keep him from biting family members by tending him yourself, and not letting anyone else interact with him. If they can't remember which rabbit to leave alone, maybe you can put a lock on his cage. Even adding something extra to unfasten (carabiner, spring clip, padlock) can remind them that this is the one to avoid.
I suggest you think about whether you want to continue keeping this rabbit at all, because another solution is to get rid of the rabbit. (Personally, I eat rabbit, especially rabbits that act nasty. But I know that doesn't work for everyone.)