I have a feeling that rehoming the dog is not an option in this case because of the boyfriend, who wants the dog there. Instead she must give up her beloved cats. What makes it worse is that the cats were there first!
try petting and soothing her and giving her treats. maybe you can use baby wipes or something to pull it off or work it loose so you can remove it without hurting her.
I'm sorry you're faced with this yucky problem.