A trans parent would likely still want to be called “Mom” or “Dad”, I assume. At least that’s the case with the few trans parents I know.
Parents don’t usually use “daughter” or “son” as pronouns, so I don’t think it would come up with non-binary children.
Do children of non-binary parents call their parents by their first name? It seems unlikely that they say “Parent, may I please have more screen time?”.
No you have it backwards, it’s DOM. As in, “I was bad so my dom had to punish me.”