I don't believe that they can make you turn your rental car in. At this time...they may refuse to pay any more toward it and put you on notice of such. You will then be paying for the rental out of your own pocket until your car is finished being repaired.
You should then be able to sue the insurance co. of the at-fault driver any out-of-pocket expenses you have due to this accident including the rental.
If you have a lawyer....he'll be able to tell you for sure. If you don't have a lawyer....GET ONE! Seems pretty obvious they are already giving you trouble and you don't need any more.
