You are not being unreasonable.
We have a lovely border collie but can't trust her around people as she is a little unpredictable. She's aged 7 yrs. Like others have mentioned some dogs are not house pets and I think this is the case with ours, She was the runt and it still very small and dainty for her age...we're often asked if she's a puppy.
She has nipped my 10 year old daughter on two occasions and attempted to do the same with me once (putting eye drops in),always pees on the floor afterwards with guilt as she's otherwise very obedient. She's never actually drawn blood. The nipping is like a reflex action that she can't control, but this just makes it more worrying. She's only done it about 5 times in her whole life, but we're very aware that she could do it again. Once was when my daughter was patting her, so she doesn't pat her anymore.
We spent a lot of time working with my daughter and dog together when she was younger so dog could learn that my daughter is the boss of the dog. Our dog knows this and is very aware of its boundaries yet still the reflex to nip comes in quite randomly. Doesn't seem to be an attack when she does it, more like a warning, she's not actually made contact with me and I think she's saying "get off" more than anything.
If our daughter had been younger like your son, I think we would have had to have got rid of the dog. Ours is an extremely well behaved and fit dog. Hubby and son are both cross country runners who train daily, so dog gets lots of exercise so there's no frustration there, it's just her nature.
It's very hard, but our neighbour had a dog that they said "turned" when it was around 5 years old. Not sure what this means? But they couldn't trust it anymore and had it put down.
Hope you make a decision that is right for you. We nearly got rid of our dog after the first time, obviously we didn't, but you can't relax around the dog the same way afterwards. We adapted our behaviour and kept ours. With your son though it would be quite hard because of his young age, can't realistically expect him to adapt his behaviour.
Would try and get your dog rehoused maybe?
SK