Sounds like so much stress. It's not clear how long this has been going on (how old the child is, how long you've been married to his father, how long the visiting has been going on, etc.) but it's very unclear why you "fought for his part of custody" if he's deployed. I agree with those who posted below that deployment is such a difficult time - but imagine how stressful and confusing it is for a child whose father is away! I don't understand why this boy is not with his mother during his father's deployment - I could see a few visits with you but I don't see the value of him living with someone who is not his parent. His dad is away, and he's also separated from his mother? That can breed a lot of insecurity in a child, no matter how nice and nurturing the stepmother is.
It sounds like maybe you are saying your husband is making you the instrument of his battles with his ex. Is that the case? You cannot be in the middle of this! If he's away, I can see why a mother wouldn't want someone else making decisions about school! I can't believe the child isn't in school near his mother and under her supervision. Maybe she's disagreeable and unreasonable, but she's got an untenable court decision preventing her from making basic parenting decisions in the child's father's absence.
If your husband has put you up to this just to beat his ex at some game, then he's showing you who he really is. Pay attention to that! Figure out why you love someone who would do that, who would put his own need to win an argument over the emotional wellbeing of his son and his second wife, and even his ex wife. If she's a terrible parent and a danger to the child, that's something else again. But if you can't prove neglect, you're a pawn in this game. Trust your gut.