you have the right to retain your own lawyer and make sure the insurance company complies with protecting your rights. failure to do so could result in the UM carrier pursuing a claim against you. ordinarily the insurance company wont tender the funds until a release is signed.
without a detailed review by a lawyer can all the issues raised in your question be appropriately addressed...nothing in this response should be construed as establishing a lawyer client relationship..the answers herein are for informational purposes and not to be construed as advice
If your insurer obtains a release for you it should protect against a subrogation claim by an underinsured carrier. You need personal coverage counsel licensed in the jurisdiction of the settlement if your insurer did not obtain a release.
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Hopefully the release your insurance company receives is well drafted and will protect you from any further liability. I am not licensed in FL, however you likely have the right to independent counsel to represent your interests. You may want to speak with a local lawyer to ensure you are covered. If not, the release does not cover you, it possible that you would have a claim against your insurance company for putting their interests above yours.
You need to demand your insurance carrier obtain a release on your behalf before they pay limits. You should do this verbally and in writing to the adjuster or lawyer handling the claim. In Florida insurance companies have the duty to their own insured to act in good faith and protect you from getting sued if they can. Also, before the other driver can sue for the UM under his policy he must get permission from his own UM carrier to accept whatever your carrier is offering which may give you additional time to make sure you are released. As an added precaution you may want to make surethat the avdverse drivers insurance carrier is named in the rlease specifically to ensure the UM carrier cannot pursue you.