My wife was in an accident and the other party was cited. Their insurance does not want to accept liability. What do we have to do?

The other party was cited with the police report. Accident happened nearly 2 weeks ago. Their insurance said the police do not know what they are doing and at first would not accept our pictures of the accident. Their insurance also was ignoring my wife's calls. The car was considered a total,loss. What do we have to do in order for their insurance to have to pay for damages and what all legally will they have to pay? We have our child's car seat in the vehicle and now it is unusable.