Thank you for your question.
Since it sounds like you and the mother cannot come to an agreement, you need to petition the court to establish a custody and visitation
order so that the rights and obligations of both parties are spelled out clearly.
Do you have a chance? Of course - the court does not favor one parent over the other, meaning both parents have equal opportunity. The court will look to do what it believes is in the "best interest of the child
." In making this determination, the court will look at a variety of factors. These include, among others, the desires of the parents; the child’s adjustment to the child’s home, school, and community; and the willingness of each parent to allow for a continuing relationship between the child and other parent. That is not an exhaustive list by any means - it's just to give you an idea. Certainly the fact that the mother allows you to have your son much of the time is helpful to your situation, but that is not going to be the sole factor the court will look at when making its decision.
I would also suggest that the court is more likely to set up an arrangement where the non-custodial parent
has the right to visitation once or twice during the week and every other weekend as well, assuming you live fairly close to one another, because they are not going to isolate the child from a parent. The goal is for the child to have both parents involved as much as possible in their life on an active and continuing basis. Thus, while you have a chance at being the custodial parent, I would be surprised to see a court set up something where a child only sees the other parent during the summer months/school breaks, unless there is a great amount of distance between them (e.g., you live in different states).
While the court will sometimes consider the wishes of an older child (it is not binding on the court, because a minor does not get to decide with which parent they will live with) at six years old, he is too young for the court to consider his wishes.
Without knowing all of the facts and circumstances involving your particular case, no lawyer could give you more than perhaps a very general idea as to your chances -to do more would be unethical. I would therefore strongly encourage you to speak with a family law
attorney in your area. You are not obligated to use a lawyer, of course, but many will offer free or low cost consultations, and there is no harm in talking to a lawyer.