To be honest, and as a veteran of a couple of decades of dog rescue, it is practically impossible to rehome a dog who has bitten a child, unless you are willing to be dishonest.
Some of my own dogs are biters - they live with me because I can keep them safe, because I do not have children visit. They are otherwise good dogs, but not safe with strangers. Most people can’t fulfil these conditions and it requires quite a lot of management from me.
Your behaviourist sounds iffy - the ones I work with, work extensively with aggression in dogs, often successfully. So it might be worth getting recommendations for someone who is an expert.
I can’t tell from a distance what is going wrong with your dog. I do know that you have three children to protect and a husband who knows nothing about training. Fixing fear aggression or resource guarding or whatever other behavioural issue you have going on is time consuming and needs consistency from everyone in the household. That’s a really big ask, particularly as your dog has already put teeth on your child - not because I will automatically condemn a dog who nips, but because managing a problematic dog, children and a husband who might well be at least part of the problem, is really hard work.
If you decide to try a decent behaviourist, invest in a crate, so your dog can be a part of the family, but no-one is at risk.
If you decide not to do that, and the rescue won’t take her back, then the kindest and most responsible thing to do is take her to the vet and send her on her way.
My inclination would be a really good trainer with extensive experience in aggression. Your husband will need to be part of this as well, because he seems at least as much in need of training as your dog. But I don’t have children to protect and wouldn’t blame you for not going forward with this.
This is not meant as a judgement, you have tried very hard and sometimes things just don’t work out. I struggle very hard to PTS a healthy, young dog on behavioural grounds, which is why I have the dogs I do.
Good luck, I hope you can work things out.