It sounds like this girl is a complete child. If she doesn't have the maturity to decide what she wants for breakfast, how can she cope with a relationship? You're better off far away from her. This may be very hard for you to get DH to realize, but he needs to know better than to fall for this kind of attention-seeking nonsense.
I had a situation similar to this with a mono boyfriend I had a few months back. It was so easy to overlook the fact that he was freeloading and emotionally manipulating me, because it felt so good to be needed and the NRE was so strong and we were so in love, blah, blah, blah. I finally dumped him after a fight that wasn't going to be resolved unless I basically told him I would never stand up for myself. Even as I was making him leave that night, he was trying to blackmail me by telling me how he would be on the streets and how he would die of exposure. It was disgusting. Despite all this, it was so hard to break up with him, and I cried a ton. It was impossibly lonely without him, and I kept haunting myself with what-ifs.
...for about two weeks, that is. Then I realized how nice it was to come home to an empty apartment, to have extra money because I wasn't supporting someone else, to not have to listen to drama and whining all the time. I have absolutely no regrets about showing this guy the door.
Your DH is still in love with GF, he wants to make everything right for her. The problem is that she has absolutely no interest in doing anything right for herself. You cannot be responsible for another person's happiness. Once your DH realizes this, things should get better.
At least he has you around to offer loving support.
Good luck figuring this out and finding someone who deserves to have you guys in her life.