Recovering from your own insurance company on an underinsured (or uninsured) motorist claim can be an adversarial situation. Your insurance company is essentially standing in the shoes of the person who caused your injury.
Your insurance company, like it or not, is a business, and they try to pay out as little as possible on claims. However, they should feel more incentivized than a third-party insurer to behave reasonably. Your insurer knows that if they behave unreasonably and in bad faith, you may have a viable bad-faith case against your insurer, which may be subject to punitive damages.