This is a terrible situation, both financially and regarding family dynamics. I cannot give you any specific suggestions because I do not know your girlfriend's income and debt load, and where she is in the debt consolidation program.
Assuming she is working with a reputable company, the most difficult time for most people enrolled in a debt consolidation program is the first six months. Generally speaking, if people can get their spending under control and develop the discipline to put money into their savings account that the debt consolidation company will use for cutting their debt, they can see the program all of the way through to debt freedom.
However, just as each person is different, each debt situation is different. If your girlfriend is really slipping behind with no hope of achieving debt freedom, then it might be time to consider bankruptcy. See the Bills.com article Types of bankruptcy for more information.
One last thought that may be a long-shot: If your girlfriend never used the cards or authorized the father to open the accounts, then she may have a fraud argument. Given that the relationship with the father is harmed greatly, your girlfriend has nothing to lose by taking all of her documentation to an attorney for him or her to review the facts and ask the fraud question. If there is a preponderance of evidence proving fraud, then your girlfriend may be able to free herself from the debt and pin it on the father where it belongs.
I hope this information helps you Find. Learn & Save.