Can I ask for Sole Custody if the other parent is not involved in the child’s day to day needs such as education, medical or extra sports?
Right now I have Primary physical custody until mediation in June. We both have legal custody but I feel my ex is not even interested in particpating in legal custody because he does inquire about anything other than his visitation.

Also if we can not agree in mediation, I would like to ask the judge if I can move of out state. We do not have any family in the state, I am disabled and can not work, ex is active duty and is gone half the year every year and then again when he is in NC he is away one week a month and misses most visitation due to his travels. Will I likely be granted a chance to move back to my home state with our minor child if the ex objects? If so, will I be responsible for half his travel expenses to see the child even though he is frequently in a diffrent state or country often?

You may seek sole custody, but unless there is some reason why the other parent cannot or is not contributing to promoting the best interests of the child, it is unlikely that the court would not outline some visitation for the other parent. If the other parent agrees to give you sole custody, the court would honor your agreement. As for moving out of state, my opinion is the same as your question regarding sole custody. The court as an interest in making sure the children have a good relationship with both parents, which includes having access to them. If you were allowed by the court to move the children out of state you may very well be charged with providing transportation for visits.

Would my transportation responsibilities be from the state of NC or anywhere he is stationed at the time?

That would be up to the judge, but my best guess is that he/she would apportion the costs of transportation by some percentage if the father’s future place of residence is subject to change. (each party pay 50% ect.)