There are no real parent / child tags. Sometimes folks fake it with hyphens, but that's often unreliable - the "design" in responsive-design refers to something very different from what's meant by design.
My advice: use as many applicable tags as possible given the constraints of tagging; start with the broadest applicable tag (bug, feature-request, discussion, etc.) and the most narrow applicable tag (say, profile-page or triage) and then fill in the gap between them (design, responsive-design, review, audits, etc.)
I know when I'm coding to attach to tags, I will normally over code the tags unless it really doesn't make sense too. My recommendation is to use the least amount of tags to get the job done, then test multiple scenarios. Add tags to compensate when you need to tighten up selection.