Will the state give his ex-wife half of the part time pension or only the pension that is named on the QDRO, which is his current full time job?

It sounds like the pension from the part-time job is a missed asset. If the ex finds out about it, she could go to court to get half. You need to see whether the part-time pension was awarded to him in the divorce. if it was, it's his.

Your fact statement is too confusing to be certain what the issue is. But, as a rule all property issues decided in a divorce case are final and permanent, meaning decisions cannot be changed later. The state cannot do anything other than what a court order requires, even if you mean that the "state" is also the employer or the retirement plan administrator. A QDRO only applies to one single, specified retirement plan that existed at the time of divorce.

During a divorce, the Court will apportion all retirement benefits accrued during the marriage, including part-time or full-time jobs.

The parties and plan administrator are to abide by the terms of the QDRO. If you are concerned about the language of the orders, I suggest you hire a lawyer.