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

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"