How Texas frames it
In Texas it is conservatorship, and it is two separate questions
Who decides — school, medical care, where the child lives — is conservatorship. When the child is with each parent is possession and access. They are decided separately, and people lose ground by arguing the wrong one.
Texas courts start from a presumption that both parents should be joint managing conservators. Joint does not mean equal time, and it does not by itself answer who decides where the child lives. Those details are where preparation matters, because the judge decides on the evidence in front of them.
How the support number is actually set
Texas applies guideline percentages to the paying parent's net monthly resources — starting at 20% for one child and rising with additional children — applied up to a statutory cap on net resources that is adjusted periodically. A court can order more above the cap if a child's proven needs justify it, and can deviate from the guidelines when circumstances call for it.
The real argument is almost never the percentage. It is what counts as net resources: self-employment income, overtime, a second job, bonuses, other children being supported, who carries the health insurance. Get that wrong and the number is wrong for years. If your order was set years ago on income nobody earns any more, that is worth one phone call.
Modification and enforcement
A court can modify custody, possession, or support when there has been a material and substantial change in circumstances since the order and the change is in the child's best interest. Orders do not update themselves, and the longer a mismatch runs, the harder it is to explain to a judge why it was tolerated.
A Texas order is also enforceable. Missed support, refused exchanges, and unilateral schedule changes are things a court can act on — but only when someone brings them with dates and documentation.
If you are afraid your child will be taken to Mexico
Say that on the first call. Under Texas Family Code § 153.501, when credible evidence shows a risk of international abduction of a child, the court must consider whether protective measures are needed. Section 153.503 lets a court order measures such as passport and travel controls, limits on who may apply for a child's passport, supervised possession, and a bond. None of that happens automatically — someone has to ask, with evidence.