I find in my work that yes narcissistic mothers and fathers can have a favourite child. This type of parent is a self feeder so they choose perhaps the nice, kind and giving child who is continuously looking for their approval.
The parent feeds off the child seeing them as an extension of themselves. The child can then become enmeshed and codependent without realising it and lost to themselves, because their conditioning is to make their narcissistic parent the priority.
Sadly in many instances the non narcissistic parent colludes, either because they have become conditioned too or to keep the peace. Perhaps they are or have become codependent themselves.
If this pattern is apparent I would encourage that the codependent parent engages in personal therapy with a therapist who understands these dynamics.
If they learn to change how they behave in the family system the whole system has a chance of changing and the child can be saved from this damaging emeshment which will affect them right into adulthood and impact on future generations.
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