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It seems to me that the two are correct.
1 Which one of these parents’ children is you?
(My interlocuter is looking at a picture with parents and children and wants to know which one is me.)
2 Which one of these parents’ child are you?
You are these parents' child. - Which parents' child are you? - Which one of these parents' child are you?
Am I correct or wrong on all this?
The question "Which one of these parents' children are you?" and "...is you" are both possible. The difficulty arises because both these sentences are correct:
You are James.
James is you.
In those sentences it is easy to identify the subject. But it is less easy in your sentence. It is unclear if the subject of the question is "Which one... chidren" or "you", and I think it could be parsed both ways. I prefer the "are you" form with "you" as the subject, by analogy with the simpler sentence "Who are you?"
The question as phrased is odd, since "parents' children" is a strange combination of words. The word "parents'" is not needed since all children are the children of their parents. There is no such thing as a child who isn't a "parents' child" (even if their parents are unknown or deceased).
If you are asking someone to identify themselves just use
Which one of these children are you?
or perhaps more simply
Where are you (in this photo)?
Your comment tells me that you actually want the person to identify their parents and not themselves. For this your question is wrong. It doesn't mean what you think it means.
If you want the person to identify themselves and their parents then use two questions (as you want two answers)
Where are you in this photo, and who are your parents?
Or if you only want the parents:
Where are your parents in this photo?
or
Are your parents in this photo? (more natural, since if you can't identify the parents, you can't tell for certain if they are there at all.)
It would be more natural in a dialogue:
Look at this photo of my 8th birthday party.
Oh that's cute. Where are you?
I'm the one with the green hat.
Is that your dad standing behind you?
No Mum and Dad are on the right. Mum is wearing the red jumper...
