It's not rainbow's job to find out why her daughter doesn't like hugs, though. Some people don't like to be touched, and furthermore, they don't like to be interrogated about WHY they don't like to be touched. Maybe her daughter has problems showing affection with rainbow, or it could be some other reason. It no doubt hurts rainbow that there is this block, but she's probably never going to know what's going on there unless she drags her daughter to therapy with her. And even then, the truth won't necessarily come out.

There's a lot that rainbow can actively do to improve her relationship with her daughter. But I don't think she should focus so much on the hugs. That's a variable that she may or may not have control over. But saying she's proud of her daughter and demonstrating this through actions are fully in her domain, and almost certainly will have a positive effect.