Can I gain custody of my son if he is getting in trouble in school, most recently an in school suspension?

I received a notice from his school that he has been defiant, disrespectful and skipping detention. He has numerous tardies and several marks for not having proper uniform. He goes to a private school. have a court order for joint legal custody and parenting time over breaks and summer vacation. He is 13. He has mentioned that he would like to live here for highschool years but his mother refuses to allow it. I live with my wife and 3 children, all have a great relationship with their older brother. It's only him and his mother where he lives, he spends hours home alone while she works. He is also failing 2 classes. It is better family structure here, my wife stays home with the kids and we would be able to put him in extra curricular activities and help him develop study habits