Yes, the insurance company still does have a duty to defend if they were initially drawn into the case You have NO control whatsoever about whether the insurance company represents the defendant. That is an issue solely between the insured and the insurance company and you do not have standing or a say in their relationship. So, you can't stop it whatsoever.
The information provided in this answer does not create an attorney-client relationship and is not considered to be legal advice. Mr. Leroi answers questions on Avvo because he strongly believes in public service from his years as a judge, magistrate, and prosecutor. If you need to ask any follow up questions because my answer did not fully address your question, feel free to call Chris or post an additional question. Thank you.
It doesn't matter where you are in the litigation. The insurance company decided to defend..they are defending. It's a contractual obligation between the insured and his insurance company. It really doesn't have anything to do with you and you have no grounds to do anything. You are not a party of their agreement.
Mr. Leroi is right. You have no control over whether the insurance company represents the defendant and really it shouldn't matter to you because your obligation and burdens are the same regardless of whether the opposing party has an insurance company defending them or not. As a general note, the failure to defend when the duty is triggered can create huge problems for the insurance company - most don't take chances with it.
The insurance company's obligation to defend depends on the nature of the contract between the insured and the insurance company. In some circumstances, the insurance company will evaluate and defend an action without accepting their responsibility to pay the claim in the event a judgment enters against their insured. This is called a reservation of rights; essentially to defend but not pay.