If someone rear end me and there telling me a part is on back order and nobody knows when it is schedule for production do I have to accept

Dear Mr. Jenkins, Your situation sounds a little unusual, but from what I can gather, the other driver's insurance company has accepted liability and has agreed to repair the damage to your vehicle; however; there a necessary part, and know one knows when it will be available.  You should request that the other driver's insurance company provide you with a replacement vehicle car while you are waiting for your car to be fixed.  You may also want to seek another repair estimate and see if the part really is as hard to come by as you are being told. Good luck, Chip Clark