Car insurance problem?

So I was in an accident about 3 weeks ago. It was the other persons fault. So I had to rent a vehicle because my car was totaled. So anyways the other persons insurance company said they would pay for a car for me. Well now a week after I have returned the vehicle the insurance company is saying they will not cover the collision insurance on the rental (the fee you pay for being under 25 years of age) so this total comes to about 200 something dollars.
So I am not a lawyer or anything but it seems like there is something wrong with this. First off they didn’t mention anything about not covering these charges while I was renting it, only after. They knew I was under 25. And second, since their person is at fault it seems like they should cover the cost of providing me a vehicle and since I am under 25 and have to pay this fee anywhere I go this would be included.
So, if they refuse to cover all the fees of me renting a vehicle should I take them to court? Seems like I have a good case, but I don’t know what the precedent is on this. And if I don’t sue the car insurance company, should I sue (or try to work it out) with the people who are responsible for the accident?