"sole" just means that he is the one that is actually responsible for them. It doesn't specifically exclude visitation.

My wife has "sole" custody of her son, yet his dad has weekly visitation, plus other rights. (Has Summer vacations with him, must be notified of school or health matters, etc.)

Remember, unless the other parent was physically or mentally abusing the child, having that parent in the kids life is still good. YOU may not want the other parent in YOUR life, but it is still good to have the other parent in the child's life. (Trust me, my stepson's bio-father is a controlling, manipulative a-hole, who mentally abused my wife for years before she got out of the marriage, but it would be torture to my stepson to rip him out of his life altogether.)