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child support is primarily determined based on each parent's time with the child and individual incomes. The idea is that the child should be able to enjoy the standard of living of each parent, regardless of which parent they are with at any given time; it is not about need, it is about quality of life for the child.
That said, if dad is not earning at his potential, there are two options: (a) the court can base child support of dad's potential earnings, or (b) the court can order dad to seek work (a violation is punishable by criminal contempt). If dad asks for support, mom would do well to ask for either or both of these options, and that would probably resolve any potential support obligation on her part.