"I ended up having an emergency C-section and there was just no way either of us could get down there and do anything."
The situation had made her "really angry and ... it's wrong", she said.
In 2012, the council decided to set tougher criteria for maternity patients to have parking tickets waived.
Council acting customer services agency manager Brendan Shea said fines could be waived in emergency situations, but matters were dealt with on a case-by-case basis.
He rejected Ms Charlton's claims, said there was no record of payment being made and she was parked in a P30 park for "half a day".
"It's such a high-use area and ... to sit on one of those [P30 parks] for half a day, we don't see as reasonable," he said.
The area was "clearly" marked P30 and could not have been mistaken as any other type of park.
The council's stance might be "seen as tough and heartless, but it is what it is", he said.
Had Mr Hurring and Ms Charlton been parked in a park other than a P30 and made some payment, then the council would likely waive the fine, he said.
Ms Charlton said she was certain her partner had made some payment, although she was not sure whether the couple parked in a P30 space or not.
She intended to fight the council about the fines because of "the principle of it".