You cannot continue to obviously and flagrantly act like you like O better. Not only are you harming X, whose self esteem is already low because other people outside the home likely also like her less than they like X, but you're also harming O.
Whenever I coach the parent of a child with behavioral problems, I ask them to take a few steps back and and look at the misbehavior as a message announcing that something in the child's life isn't working.
When in front of each of your children, you and your new partner must present a united front. Whether you agree or disagree should be saved for private moments. Both sets of children need to see you two working together as a strong unit.