You've misquoted the amendment. It is "the right to peaceably assemble." The Constitution was written before the invention of grammar nazis, and before Victorian snobs decided you couldn't split an infinitive verb.
Please be more careful before posting in the future.
You may find it interesting to examine the original text of the Bill of Rights, where the first amendment appears as Article the third: http://upload.wikimedia.org/wikipedia/commons/7/79/Bill_of_R...
(Article the first has never been ratified. Article the second was ratified in 1992. Articles three through twelve were ratified as the first ten amendments in 1791.)
Interestingly, to me at least, I read the quote, and remembered the text with a split infinitive. To check that I was right, I googled the text of the amendment, which google helpfully displayed above the search results. Seeing that I was right, I copied and pasted the text from google into the comment box here. What I did not do was read the whole text that google provided, only the relevant clause. If I had read the whole thing I would have realized it was a paraphrase rather than the actual text. I offer my humblest and deepest possible apologies to the OP, and to you.
However, I probably won't be much more careful when posting in the future. I try to keep my statements of fact on HN accurate by checking at least some source. In the end that's as far as I'm going to go.
"To boldly go where no man has gone before"
"We are determined to completely and utterly eradicate the disease."
"She wants to gradually get rid of her teddy bears."
"Writers should learn to not split infinitives."
It's also not always possible to eliminate the split infinitive, or the infinitive, without changing the direct or implied meaning of the sentence. "She wants to get rid of her teddy bears gradually" works fairly well.
"Boldly going where no man has gone before" is close, but doesn't capture the same challenge, summons, call to action as the original. Nor does it sound as pleasing.
So, what would we want?
"Boldly to go where ..."
or
"To go boldly where ..."?
To be really clear that 'boldly' modifies 'to go', it's easiest to split the infinitive.
Your
"She wants to gradually get rid of her teddy bears."
is terrific! There's just no good other place to put 'gradually'!
In case you misunderstood me, for grammar for English, really I have no sympathy for what the heck Latin did!
She wants to get rid of her teddy bears gradually.