When to use "not to" and "to not"

I wonder what "structure" should one use, "to not" or "not to"?
Is there a difference? is one more accepted?

"It's human nature to not do what someone else wants"
"Like I needed another reason not to like dogs."

Can those sentences be re-written as:

"It's human nature not to do what someone else wants"
"Like I needed another reason to not like dogs"

Answer: Yes.

Proviso: But they suggest slightly different emphases, or occasionally different semantics. For example, with the negation you may be intending to express antipathy instead of apathy.

You might move the negation onto the verb to clarify:

"Like I needed another reason to dislike dogs"