When I was 14yrs old I became pregnant by another teenage boy in my high school. My father was unsupportive and he was my only parent. I moved in with the child's father and his mother when I was 4 months pregnant. The father of the child moved out a month after the baby was born due to not being able to overcome a drug problem. We dated for a few months after that but when no progress was made in his rehabilitation I discontinued visits with him. His mother and I raised the child together for the next 2 yrs. At 15 I breastfeed for 11 months and stayed out of school. The year after that I resumed high school maintained a 4.0 GPA but developed a relationship with the father's best friend. I had thought the friend was rehabilitated but appearantly he had just changed substances. During our 6 month relationship I began recreationally using painpills, after my daughter would go to sleep, and on the weekends I would stay at the new boyfriend's house.
After the six months I realized what I was doing was wrong and it should not be around my child. Because I felt cheated of my teenage yrs instead of stopping the drug use and continuing to live with my daughter I decided to move out. I stayed in the home until her father now rehabilitated came to live with his mother again and help out. He felt 2 yrs later.
I moved back to my home town but kept contact with my child and her grandmother. For the next three years I sent money when possible, every few months, and had at least 5 visitations per year.
Two years ago I joined the Army. I have done extremely well in this environment. Since my enlistment I have sent child support every month, extra money when possible, and phoned my daughter every two weeks at least. When I am given leave from the Army I visit with her.
The grandmother and I have a good relationship, but when I bring up the idea of more visitations, I am shut down. I have never signed any papers giving the grandmother custody. My child is now 7 yrs old, she knows me as her mother and that I can not be with her because I am in the Army. How much ground do I have on requesting more visitation with my daughter... and eventual fulltime custody?

The best you can do is apply for custody - or a return of custody - to your local Family Court. You will prove you are stable and not a danger to your child; your Grandmother will attempt to prove that you are unstable and a danger.

The Court will listen to both sides, undoubtedly appoint a legal guardian for the child, and issue an Order.

How if your Grandmother obtaining medical treatment for her, enrolling her in school, without legal guardianship?

Paying support when you can and not regularly is not going to endear you to the Court - the Court will take the position that the child has to eat every week.