The fact that police officer cited the other driver means nothing as police do not determine the fault but instead insurance company does. From your description it sounds like you have comprehensive insurance. Did you have a stop sign or only the other driver? From your basic description you had right of way and were established. Next time you talk to the other insurance company I would make sure to mention that you feel the other driver failed to yield to you being you were established, he run a stop sign(if there was one) etc. You basically need to push the other side to accept liability. Also your insurance agent should be in constant contact with them.