In Texas visitation cannot be conditional to the payment of child support. Obviously, because a noncustodial parent should not be barred from seeing his child if he falls behind on his payments. He could be barred for months depending on his arrearages.
What if a noncustodial parent falls behind on Supervised Visitation monthly fees, and thus does not get to visit his child because excessive outstanding fees barrs participation at the Visitation center. Isn't that like barred visitation because of unpaid "child support"? What's the statutory definition of child support?
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Child support is money that goes to help financially support the child. Supervised visitation fees are fees spent to support the facility that is having to provide a place to watch the child and the parent, plus a supervisor, etc. So you can't look at the money spent on supervision as child support. It literally does nothing to support the child.
If the supervised visitation is too expensive, then perhaps try to find a place that has a sliding scale, or see if the court may agree to a mutual friend or relative supervising.