Liability of causers of accidents vs own Kasko insurance

Hello dear car friends, I had a serious accident with my Golf VI on Feb 12 in Berlin (2 years old), at a big crossing the causer took me at the left turn from escaped direction the driveway, I could not avoid and we had a crash at about 50km/h. The good thing is neither to him nor to me what happened, but the cars looked bad. The car was then directly next Monday by an expert in my workshop in sight In addition, I have reported the damage of the insurance company (Alliance) of the accident seller. The repair costs will amount to approx. 13,300 EUR, impairment is 1,300 EUR. The vehicle is not ready for driving at the moment. My problem is that the cause of the accident has reported to the insurance company that I was driving too fast, so the insurance company does not issue a repair release and waits for the police report, nobody knows how long it will take. I get a rental car. only replaced for the duration of the reperture (is indicated with 6-7 days in the report), i.e. I am currently standing without a car since My lawyer said that there is no possibility to speed up the matter, I could of course take advantage of my comprehensive in the case and assign the damage, I would then, as a sidekick, claim the costs (share ownership and the upgrade of the SFK) with the opposing insurance. That is of course also negative for me because the damage-free My question is now whether someone still knows how to put pressure on the opposing insurance company. I honestly can’t understand why there is no rental car claim for the entire time until the car is repaired, as I am not responsible for the accident. Thank you for your help.