Sorry to resurrect this thread but just wanted to thank prh47bridge for all the advice, which we followed. DD made the representation which was rejected and so went to the Tribunals.
Apparently one ticket had been written by a traffic warden and the other was issued automatically by some camera or other.
Now, it was complicated because they actually did post out the 2nd ticket within the 28 days but DD, on receiving it, put it aside as, as far as she was concerned, it had been paid a couple days prior to receiving it. But she'd paid the first, handwritten, one.
She hadn't looked closely enough to realise that they had different numbers and were, actually, on inspection, some 8 minutes apart!
She argued that it was the same offence (she'd been parked there for just under one hour all told) and that no-one expects to get two tickets for the same offence, hence why she hadn't scrutinised the second ticket more closely, she had just assumed the payment and the letter had crossed in the post.
It's taken a long time but she's finally off the hook and didn't have to pay the second fine after all. 
Beggars belief that they're paying a warden, utilising a camera and then wasting tax payers money arguing the toss to boot. No wonder councils never seem to have enough money for essential services 
Thanks one and all for your replies.