Courts don't usually take children away from the parent and home they've had for 12 years on a child's whim, though there a FEW states that give a child a legal say at a certain age.
"She is not married and I am so I hope this works in my favor"
Umm, were you married when you got her pregnant? One cannot conceive a child, then marry someone else and attempt to take her child from her. So, no, you have no more rights to the child by being married than a single father/mother would. Though it's common for a father to think being married might give him more rights...it doesn't. Courts no longer discriminate between married and single in this world of singles PROCREATING..of which you were apparently one.
Unless the child lives in one of the few states that allow him to choose at a certain age, it's extremely unlikely his mother would lose custody on the basis that you are married now and the child wants to go with you.
PS. It is also common for a child to want to live with the other parent, where it is more of a vacation than the bored, sameness of his home. Kids usually get away with more while visiting the parent that doesn't see him often.