well in the collision select only these parts...i´m not sure if you need to select something more because i´m not dynamic expert...just what i know...sorry talking later...going to dinner! 
In the cloth room, you can edit constrained group, and paint a few of the collar vertices, and add those to the constrained group....it looks like it's sliding off her shoulders, so I think there needs to be some sort of constraint to keep it up on her shoulders.