some families can be bullies, it's a real shame.
no wonder the girl has self esteem issues when her parents, the people who are supposed to support and care for her are saying such destructive and insulting things, though this is essentially the same "trick" that controlling possessive types use in their relationships; "beat the other person down emotionally so they think nothing of themselves then they'll do what you say". (slightly ranty yes,but a friend of mine has an awful family who beat her up based upon her boyfriends race)

but on the other hand, if they really were that controlling and possessive would they really have let you come to stay? and you seem to have a good relationship with them so it seems a little strange that they would say things that would undermine the relationship. can you be sure that they really have been saying those things to her? it's possible that it could just be an excuse because she's afraid of coming to stay with you.