Are you a parent who wants the best for their kids?
Are you a parent who wants the best for your kids?
Are you a parent who wants the best for their kids?
Are you a parent who wants the best for your kids?
Are you a parent who wants the best for their kids?
The question is detached from the 'parent', and refers to 'you' (the subject being questioned) as one parent, among many, to group you.
Are you a parent who wants the best for your kids?
The question is attached to 'you' (the subject being questioned) as a singular parent.
Conclusively, both are grammatically correct, the point of reference differs though. 'their' & 'your' would be a difference in person, that is, third person, and second person, respectively.
It is worth noting that: it is more appropriate, given the context of an interview, a dialogue, or a questionnaire, that you should refer to the person being questioned in the second person perspective.
The first is correct. It asks for parents who want the best for their [own] kids, and asks you whether you are such a parent.
The second asks about parents who want the best for your kids. That is, from the perspective of the parents being referred to, parents who want the best for other people's kids. That's not what the asker means to ask about, so it is not a correct way to word the question. Yes, it's grammatically correct, but the important thing is that it's not a correct way to express the intended question.
Both constructions will be equally understood by many English speakers but there may be regional preferences for one or the other and they may be interpreted as slightly different in meaning. The first construction may be interpreted as "a parent who wants the best" while the other might be interpreted as "you who wants the best". Deconstructed to "are you a parent, are you who wants the best".