I’ve wondered about this for quite a while now: is it incorrect to have statements like “to not”? My mother says there is no such thing as “to not,” if so, why not?
For example, here are two ways to request someone to work harder:
“Try not to be so lazy.”
“Try to not be so lazy.”
Is the second way of saying things incorrect English? It seems that the first one is saying “do not make an effort to be lazy,” but of the two, is only the first one correct? And if so, why?
The first phrase is the correct version. Never split infinitives. (To eat, to cry, to walk, etc.) The verb should always follow the “to” in your sentence without any words in between.
I’m no grammarian, but it’s my understanding that the “split infinitive rule” doesn’t really exist. What’s more important is clarity, and how well the sentence flows.
http://www.bartleby.com/64/C001/059.html
To my ears, anyway, the second one sounds slightly better. That’s probably just me, however. YMMV.
“Do or do not, there is no try” ? 
I actually think your first example (“Try not to be…”) flows better to my ear … maybe because of the split-infinitive rule. (Or rather, “rule”.)
For a logical standpoint, the second one is somewhat more clear – it tells you what to (try to) do, not what not to (try to) do…
To summarize this page from the American Heritage Dictionary (4th ed, 2000), there is in general little wrong with a split infinitive per se. There are times when a split inifintive makes for an awkward word order, but there are also times when avoiding a split infinitive makes for an awkward word order. In general, one should appeal to sentence flow, as Cabbage stated. For those who want to avoid split infinitives, it’s usually easy to do so, but for the rest of us, there’s no pressing need.
Avoidance of split infinitives is not a hard-and-fast grammar rule, but it is often taught like it is, though this is becoming less and less true. In my experience, many people who think it is necessary to avoid split inifinitives at all costs are the same people who believe that “funner” is not an English word.
Neither example is incorrect. I’d prefer the first, but the second isn’t wrong.
No modern authority on English grammer thinks a split infinitive is wrong. The only warning is not to split them with a phrase (e.g., “He decided to often on a Sunday go to church.”), since that’s always awkward.
Consider “To boldly go where no one has gone before,” for example. This is much preferable to “To go boldly,” simply because it keeps the iambic rhythm of the first half of the sentence.
BTW, the original justification for the rule is this: Latin infinitives are one word. Extra points to the student who can explain the reason why they thought this fact had any relevance (there was one, but it is total nonsense).