If your case is in Irving, your case is before a specialized family court judge (as opposed to a general jurisdiction judge as in Collin County or Denton County). The judge who hears you prove up your final decree will almost definitely be the elected judge of that district while your temporary orders were almost definitely heard by the associate judge for that district. Therefore, when you go prove up your case, the judge may not know that supervision is in place, unless there is an AJ report on file that the judge might take a look at.
Therefore, you can probably get away with what you want to do.
HOWEVER, you need to ask (1) why did the court order supervision or why did you ask for it in the first place? (2) What has changed that you think supervision is no longer necessary?
The Texas Family Code says that judges are to approve agreements between the parties if the agreement is in the best interest of the children. The Troxel case instructs courts that fit parents are presumed to act in the best interest of their children. Thus, if you and your wife present an agreed decree and you are both prepared to testify that the agreements are in the child's best interests, the court will very likely approve your decree.
If you don't have attorneys, you should hire an attorney to sit down with the two of you and read through your final decree to make sure it really does what you want it to. At least 25% of my business comes from people paying me to fix decrees that no attorney every reviewed but then later problems arise in enforcing the decree. A few hours of attorney time is a good investment at this point.
There is no guarantee what the court will approve. You will need to provide bailed reasons if asked what has changed in order for to you to agree to unsupervised visitation if asked. The court will always rule in the best interest of the child
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