Could a Father or mother move out of State that has Primary Legal and Physical custody ?

With permission of the other parent. With permission of the court. And of course if the child custody order allows.

Ok but there Lawyer told them it was OK and all the other parent has is phone contact with the child Through a court order

The issue here is what does the actual custody agreement say.

Since the other parent only has phone visits ( why?) this is not going to interfere with their visits. BUT.
Is this a temp visit arrangement ?
Has the other parent already moved out of state?
Why only phone visit?

Primary Legal and Physical were granted to the Father by the Courts due to the Mother's other Partner has pending charges against a minor child not of either of the party's as it states on the Order Mother may Exereise daily telephone contact with child Pending criminal charges ( Endangering Minors ) againast mother's Fiancé must be resolved at future conference Primary Legal Custody Father Primary Physical Custody Father

In this case I would seek the courts permission. As you have stated there are future decisions pending. If you were to move out of state you will have to return to the state to fight any custody changes.

Yes as they told the Mother once the issuse's were dealt with on her side then she could take action in court again which as far as I know nothing has happen I get the oh everything is cleared up now but no proof has been provided and nothing about a court date either all I get is it's dealt with what could we do about her seeing are son all I ask is for the proof that it was dealt with for the safety of the child