When does the claims Adjustor for a rival auto insurance company has to appraise my totaled vehicle?

Their client was issued a summons. The company has not accepted liability. My car is accruing daily storage charges. 2/2/19 will be 30 days. They want to move the car if they can access the black box. I was advised not to give them access. What can I do? They wrote and told me I'm responsible for moving the car and I must allow them to inspect it. My insurance company is limited since the car has no collision or comprehensive. What are my best options? Move the car out of pocket and try to recoup my expense. The storage fees are at $1000.