How do we write up an agreement for the non-contested relocation with minor children?

Any agreement reached between yourself and other parent is not enforceable unless it is recognized by the court, incorporated into a judgment and made legally binding. So, I recommend you find a lawyer you can both agree to meet and have the papers drawn, have the lawyer file them and request a hearing date on the application and have a court accept them and incorporate them into an order/judgment after a hearing. There in a wrinkle to your joint agreement plans: if you have not been adjudicated father of the children-- the bad news is she could, conceivably, just take the kids out of the state and you would have no legal recourse, or it would become much more complicated. If there has never been a prior proceeding and judgment that named you Father you will have to file a Complaint for Custody/visitation and go through the process of adjudication. THEN the Agreement can be put into place with your specific request for tax relief and visits, etc.

I think you are asking for too little. In exchange for permission to move, there are other fair and reasonable requests you can make. You are selling yourself short at the expense of the father -children relationship. If I were your lawyer I would not approve of this transaction at all.