I've been there OP, hopefully I can give you some pointers.
You were passed to a claims management company who will deal with your case. These are (as I found out) a bit like insurance debt collectors, middle men who effectively buy an easy claim with the intention of recovering costs from the at fault party. However there are a few issues with using them. I was sold the "you won't pay any excess" line, and I fell for it. I was also rear ended by a kid at a roundabout, nobody else involved though.
Because I had a like for like replacment car, and mine was a 4X4 auto, the only similar spec car Enterprise had was a huge Mercedes 4X4, at £109 a day. I signed the forms and all was well, I thought. My car was in the garage for seven weeks, the hire car bill was £5k by this point.
I got my car back eventually and thought that was the end of it. Wrong.
14 months later I got a letter from the the management company asking for £6.5k, they couldn't recoup the cost of the claim because the kid driving had been deemed to not have valid cover. And they referenced the T&C's I had signed on the hire agreement.
Long story short, I did contest it and they did back down, but only after I had my solicitor get involved. It was stressful and protracted. My advice to anyone who is offered a claim managment firm is to say no.
Anyway, your case will be complicated because there is another car involved which will (if my insurance guy was right) try to claim off YOU as you technically rear ended them! Then you will have to claim additional loss from the kid person who rear ended you. Complicated.
I suspect that's why there is such a mess in your case. Be preemptive and get legal advice, this could get very expensive as you also have an "open claim" on your policy and will get crucified come renewal. Be prepared for 4X your pre-claim annual premium.
DO NOT respond to any letters from any other company involved except your managment/insurance company. They will be sneaky and send you "questionnaires" about your opinion on who was at fault. This is to use against you in court. I had about four of them.
Good luck.