It appears that you cannot claim your girlfriends daughters as dependents because they are not related to you and they did not live with you for the entire year, all 365 days. They only lived with you 5 days a week.
Since the daughters lived with your girlfriend more nights than with their father, your girlfriend is their custodial parent. The father cannot claim them as dependents unless your girlfriend gives him a signed Form 8332 giving him permission to claim them.
If your girlfriend files a tax return, she can claim her daughters. If she does not file a tax return, and does not give the Form 8332 to the father, no one can claim them.
If your girlfriend has no taxable income and is not filing a tax return, it seems like she might as well allow the father to claim her daughters. Neither she nor you loses anything. If she does that, she should sign Form 8332 for only one year at a time, because the situation could be different in future years.
