Right, you need to be quite bullish with your insurer and advise that they are not to prejudice your position. You have paid a premium for them to indemnify you and you expect them to stand by you and not run for the hills just because liability is disputed. I presume you have already pointed out the factual points you have stated above which should lead them to believe that your version of events is far more likely on the balance of probabilities. Do you have any uninsured losses to recover such as insurance excess? If so, would you be prepared to issue proceedings through the small claims court and attend court to give evidence to fight your corner. As it would be a small claim you dont need to worry about legal costs if you lose.
Unfortunately, if you dont show to the insurer that you are willing to attend court then they can agree to the 50/50 withut your express consent as the insurer has a right of subrogation.
It is a sad reflection on society when people cant just hold their hand up when they genuinely know that they are at fault