Car insurance claim denied

I had a vehicle insurance on feb13 2016, the insurance company took their own time in handling the claim. I explained to them what happened, gave all supportive information needed. The senior claims consultant continue to check my ******** record-not part of the claim-no alcohol was involved at time of accident and no samples were provided. He mentioned that because I had past incidences of driving under the influence, he will need to make more investigations. He enlisted the help of a crash expert to determine the speed I was doing at time of impact. I was driving on a 60kph zone and doing 50kph at time of accident. The expert gave a report that I was doing 100kph. If I'm not mistaken, any car that gets hit by the opposite vehicle will have a compound speed. He then mentioned that because of the speed and that my rear tyre wasn't in good condition they will deny my claim. I had insurance for 5 years with same company but they negate their responsibility to pay ou