The change of perspective and who the "I" is in the situation doesn't make sense.
Who is paying child support to who? Who is the child living with? At one point you say you have "almost no authority or even correspondence with child" but then you go on to say "the marital property that I and child reside in"
Generally the court will take into account the earnings of both parents. To many details are needed to know what a specific court/judge would do... Your best bet is to seek local legal counsel.

