I don't think parents expect swabs... unless they are being offered to every Tom, Dick, and Harry. If we stop offering these stupid tests, people will stop expecting them as much.
I've never had a major issue with just saying to the patient's parents, "Clinically, your child has the flu. If not the flu, then some other virus that we treat the same way. So, let's treat it by...." and then proceed with your treatment plan. Ninety percent of the time the parents are happy after this.
If they buck and complain and ask about the swabs, just say, "Here's the thing. The X swab isn't that useful. You can get false negatives, and remember, we're treating your child anyways, because we know it's the flu or some other similar virus. Getting the swab won't change our plan, and it will just keep you waiting here in the ER for another couple hours... And we'll be in the same spot once those results come back. Because remember, we're gonna treat your child no matter what. So, I recommend that we start the treatment right away. Do you have any questions for me?"