I like to imagine that Mokou fights with Kaguya due to a twisted desire to become or possess that which her father wanted. However over time, as her family disappeared, her body changed so drastically, and she found herself in a new world it changed into a desperate attempt to maintain her sense of identity. So she overacts her grudge against Kaguya as that relationship is all she has left of who she was.
I like to imagine Kaguya is emotionally deadened after spending her time as a doll, simply shipped around for admiration amongst the courtiers and surrounded by aloof genius types. Being mostly isolated for centuries with few new experiences she has become wholly jaded and has no motivation. But Mokou always attacks her with emotions flaring, so she provokes the girl, living vicariously through those emotional outbursts, leaving the two of them in a twisted dependence, beating back the pathos of eternity.