Let's break it down a bit. "His speech was uninhibited, unprepared, and frankly insulting to half of his audience." So let's boil it down. The speaker says other person's speech was uninhibited. It was unprepared. Then comes the idea we are focusing on: It was frankly insulting. For the purpose of answering your question, the rest is unimportant. I always find it helpful to remove the extra information when dissecting a descriptive sentence like this. Now we can see that his "speech" is what's being described as "frankly insulting." So we have the adverb "frankly" describing the verb "insulting" with no commas around the word "frankly" to stop it from describing our verb. Your first interpretation is correct! Good job.
Now for the alternative interpretation you present. If I were the writer and had intended to express my opinion that the speech itself was insulting, I may add a comma after the word "and" as well as the word "frankly". This would be to show that the speaker was stating that he was being frank about what is said next. Remember, this sentence is being spoken so rules of grammar will be bent a little. Of course, that's not the only way you could express that the speaker of the sentence was being frank. You could reword the sentence to make it a bit clearer, or the person the speaker is talking to could ask for further clarification. But, like I said, it's spoken English, and who of us sticks to the rules when we speak, right?
As for a linguistic term for describing the sentence itself, I am unaware of one. The word "sentence" is a noun and any word describing a noun is considered an adjective. However, try researching it online, or perhaps another tutor may be aware of such a grammatical term. Otherwise, the word "frankly" in the original sentence is simply an adverb describing "insulting".
Thanks for posting your question! And remember, when deciphering the mean of what someone is saying in a long or really descriptive sentence, try to boil it down to the basics like I did above. I know it helps me!!