It sounds like you have a dog who is a resource guarder. He guards things that are especially valuable to him, in this case his ball or bone. It's a natural and normal dog behaviour that some dogs do more than others. But it's a not a behaviour that we, as dog owners, want them to do. Resource guarders can usually be trained not to guard, or if an owner has identified what's being guarded it's possible to not let the dog have those items, leaving him nothing to guard.
It doesn't mean that he's aggressive. He's a resource guarder and that's very different. I would imagine that he's given warning signals in the past (which may have been subtle and missed by you and your family) so now feels that he has to go a step further and bite because his warnings have been ignored.
With regard to his reactions to other dogs, baring teeth is a warning. I don't know the circumstances so I can't comment beyond that. He may be feeling anxious around other dogs for some reason and because of that he can't easily stay calm if he's close to them. Again, it doesn't mean he's aggressive, but he needs somebody like a behaviourist to assess what the problem is and to help him.
I can understand that with young children around you're worried. I honestly think that with some help you could train him and help him, but if that's not for you I'm not going to criticise, I'm just going to ask you to please rehome him sensibly. He would be best going to one of the organisations already suggested, or somewhere similar. They will have the knowledge and time to assess him and train him before placing him with a suitable family. They will also be there as a backup for the rest of his life.
If you sell him privately, or even give him away, you run the risk of him going to people who will immediately sell him on at a profit, or even perhaps use him as a bait dog in a dog fight. There are some very clever scammers around. Even if he goes to a lovely family, how can you be sure that they have the experience to help him through his resource guarding?
So please, rehome him through a suitable rescue so that you know he'll be found a suitable and loving home by experts.