A Court of Appeals panel's ruling Tuesday says a judge must consider ordering the Victoria native to pay more than the children's "basic needs."
The court also upheld a judge's order barring the couple from disparaging each other through social media.
It said Alejandra Amarilla Nash used her Twitter account to make a "biting criticism" of Nash after their divorce was granted.
The ruling says the order doesn't violate her free-speech rights because both agreed to limit their speech under their joint custody agreement.
The couple divorced in 2011. They have a son and two daughters.