Should I hire my own attorney or let the insurance company attorney handle my case?

I was in a car accident several years ago and am currently being sued. The amount the plaintiff is asking for (70,000) is less than my policy limit (100,000), however my insurance company is choosing not to pay as they feel the amount is unreasonable. The insurance company has assigned me a lawyer who has been taking care of paper work, filings, and everything. This is now to the point where a deposition has been requested. My question is: should I hire my own counsel? Does the insurance company appointed lawyer truly have my best interest in mind or the insurance companies? In my opinion since the requested amount is within my limits the insurance company should just pay it, and this can all be over with. Any advice or recommendations would be greatly appreciated.