To anyone trying to raise a child alongside a HPD, I am very sorry and wish you the best of luck!
Here are some suggestions for trying to minimize the damage of an HPD (damage: the child may grow up not really knowing who they are, not trusting their feelings/thoughts/judgements of themselves and others,thus, they may be quick to heed an authoritarian voice, because they were taught that the authoritarian figure - the HPD - has all the right answers, Growing up with a controlling and over domineering voice will inhibit the development of the child's voice, leaving the child lost and confused as an adult)
1. Affirm everything!!! This could not be more important. The child while being with an HPD will be told that their needs are secondary and that their needs/emotions must be want the HPD wants. It is therefore important, whenever you are with the child, to let them know that their feelings are real and that they matter. eg. child is scared of the dark, response "I understand that you are feeling scared right now, its ok if you feel scared, but I want you to know that I am right here and I love you very much, and I promise to do my best to make sure that you are safe tonight, is there anything I can do right now that would help you feel more safe" I know that this may be difficult and will require you to be very vigilant in your responses, but I promise that it is wort the effort.
2. The child is going to love the HPD parent, its what children do. however, they may wonder if its OK to love them, and may feel hate and love for the parent, these dualistic feelings are very confusing for children who tend to think in black and white, your jobs is to help the child develop more nuanced perception/thoughts/feeling. it is very important that you address this in a manner supportive of the child's feelings, do not trash talk the HPD parent, or make the child feel like they should hate/or love, the HPD parent . An appropriate response might look like this " I know you love your mommy/daddy but I know sometimes he/she does things that make you feel angry or sad. Mommys/Daddys aren't perfect, and sometimes they make mistakes, and its ok to love them but be mad at them too. Sweetie, i will always be here for you if you want to talk about this or anything else, do you want to talk some more?"
3. Address the wrong comments by the HPD- The HPD may tell the child that something about the child or something the child did was wrong, stupid, ugly, etc... Whenever you hear about it (or even if the HPD said it in front of you) you need to correct it asap, even in front of HPD (while not trashing the HPD) ex : " honey, i know [blank] said ...... [you were ugly] I'm sure that they didn't mean to .... [hurt your feeling] , but even though he/she probably wanted you to ....[loose weight, wear different clothes] that was still a pretty hurtful statement, and its ok you think/feel that he/she hurt your feelings, and despite his/her intentions to help, I need you to know that you are wonderful just as you are, and you don't have to change your ...[weight] , [loosing weight] won't make you more wonderful because nothing could be more wonderful than who you are right now. "
4. Let the child lead, really. The HPD parent will dictate everything, including how time will be spent. He/she may give the guise of letting the child choose, while really maintaining control (aka, the child says lets do X, HPD says you dont really want to do X now do you, wouldnt you rather/have more fun doing Y). So allow the child to make decisions : what to eat or not eat, when to eat, how free time should be spent, etc.... And I think it would be really helpful for you to look into "parent-child interaction therapy" similarly you should spend time with the child playing, but instead of you taking the lead, let the child, eg: if the child wants to play pretend tea, ask them how you should dress and what things you should say- let the child become the "adults" and direct you, as if you were a doll who must obey the child's wishes (try doing it in a place and in clothes that you don't mind getting dirty, you dont want your fear/worry of mess get in the way, children pick up on it)
5. Seek therapy, for both you and the child (if a younger child, I recommend you find a therapist that is trained in child-centered play therapy, if you need help finding one, contact the center for child-centered play therapy at the University North Texas). It is important that both you and the child have a safe place to process your interactions with the HPD and to develop strategies for minimizing any harm from interactions with the HPD