Perhaps I'm being stupid, but it's still not clear to me exactly what happened, in regard to whether it was a full-on bite or a warning snap. OP has said her son's arm is marked - was the skin broken, is he bruised and have you taken him to dr/A &E?
Homes can be found for dogs that don't get on with DC - one of our dogs would not be homed with children (we don't have any). However, it takes time, and unfortunately this time of year is one of the peak months for many rescues - lots of abandonments as people go on summer holidays or find the combo of kids/dog too much like hard work.
OP, it will be possible for you to rehome this dog and I understand completely that you are shaken, upset and very worried. But emotional blackmail to rescuers isn't helping. Most people involved in rescue will do their utmost to help in circumstances like this (many are parents themselves) but can only work with the resources available and as others have said, you threatening to kill the dog you allegedly "love like a baby"
doesn't help. Over the years, I've dealt with several rescue cases where owners have threatened this, and in every single case, the dog has been mysteriously fine and gone on to be successfully rehomed.
I won't repeat the list of specialist rescues you've been given - there are lots of breed specific ones that have already been linked to for you. I hope you are able to find a good outcome soon.
If you do surrender to a rescue, it's very helpful if you can get together your dog's health records, microchip details, whether neutered, vaccination cards,details of training classes attended, lists of any medications, allergies, food preferences etc. It will also help the rescue if you are willing to drive to drop off dog to an emergency foster placement, and are willing to provide a relinquishment donation. Rehoming your "baby" will take a great deal of time, effort and resources for the charity concerned.
Finally, as others have said, DO NOT surrender to a pound - this will be a certain death sentence, with the added knowledge that your "baby" will have spent a week in noisy kennels, alone and very, very stressed before being led to face the needle by a stranger.