I think the base issue is that Kansas doesn't consider the lesbian relationship as legitimate and binding. If this same situation had played out with a female mother and an male, but infertile, father, there would have been no question that both bore financial responsibility for the child regardless of the method of conception. Because the relationship is not recognized, mother mother and mother father are not jointly responsible, and a third party is brought into the support equation.
I don't care about the morals, traditions and threats of divine retribution; the state is doing a disservice to all citizens by not recognizing the non-traditional "marriages" under common law. In this case they seek to recoup $6000 from a third party, and will no doubt pick up far more than $6000 in legal expenses as this nonsense winds through the courts. Make the non-traditionals bear the same social responsibility as the more conventional family units. I am less concerned about any moral implications of such relationships than I am about the lack of responsibility that is afforded to participants in the non-traditional relationship because the state fails to recognize them. The state's perverted thinking on this matter brings real costs to the people whose moral values they are allegedly protecting.
Marry them, tax them, and let them bear the cost of their choices like the rest of us. Share the pain.