"Kleidung" doesn't really mean "dresses", it means "clothes" or "clothing". I think you really need to go with "Kleider" here if you want to say "dresses".
Is it "ihre" and not "ihr" because it's "her" and "ihre" refers to feminine ownership, or is it "ihre" becuase it's "Kleider" and "ihre" refers to ownership of multiple items?
I beleive it's Ihre becasue although Dress is Neuter, it's plural here so the E goes on the end to make it feminine. If it was one dress I beleive it would be Ihr. Please correct me if I am wrong!