Being active duty military, what are my chances of winning custody of my children?
I am not licensed in your jurisdiction but will answer your question based upon my experience. In my state, you would have to advise the court of your deployment scheduled and/or the likelihood of you being deployed.
The main concern for the court, in my experience, with activity duty military is that in the event you are deployed, what would happen with the children and what the alternative living arrangements would be.
Certainly if you live close to mother and it would be an easy transition that she could care for the children while you are deployed, this should allay the courts concerns. Further, if it is likely you will not be deployed and/or you are considering leaving the military, you should notify the court of the same to show that you will, potentially, have a consistent and stable home.