I think you're an awesome friend to be providing her with this level of support.

I also think you should re-frame what you're feeling. You don't dislike/hate/resent the 2 year old - its his behaviour you dislike/hate/resent. Don't beat yourself up about being an awful person. That kind of behaviour is hard to tolerate and is probably preventing you from feeling much of a bond with him (beyond the intellectual knowledge that he's had a rough time so far). It would be good to focus on his behaviours (actual examples) in any discussions you have with your friend about him. His behaviour and her feelings. So it would go something like "When X does a, b, c, it affects me/my kids in e, f, g ways and I can see it affecting you too".

I definitely think you guys need a third person or service involved. One that's trained to deal with these kinds of behaviours in 2 year olds. A pp was right, 2 is awfully young to be making any kind of formal diagnosis - it's shaky ground - but behaviour problems can be managed and improved over time.

I really hope that she is able to access some kind of service or assessment for him that leads to greater support for her (and you and your DH) as well as practical strategies to manage him. Whether you still need them to move out, only you can answer. You have to do what's right for your family - just because they don't live with you (if that's what you decide) doesn't mean that you still can't provide a large amount of support.

Good luck hun. That's a really difficult situation to be in.