I know you do not want to hear this, but most of what you written is not relevant to a custody matter.
Most of it was before you were married. Cigarettes, while not healthy, are not illegal. Her saying she will give you custody is not relevant. Her being in debt and having a criminal past doesn't matter...at all. Unless her crime involved safety of a child, it typically has no bearing on a custody determination.
The chance of you gaining sole legal and physical custody and having a court give you permission to take the child 2000 miles away from the mother is not very likely at all.
Custody laws are gender neutral, but it is not likely for you to be given sole custody or primary physical custody. The courts are not going to cut Mom out of the child's life, anymore than they would cut you out of the child's life.
You should at least consult a local attorney, one who is familiar with local laws and judges is your best bet to know what your chances are.