Diane Fraser, 43, was ordered to pay £164.60 or sheriff officers would call at her home.
The fine was issued in July last year when Mrs Fraser and her family – husband Ross and children Alana, 4, and Rory, 7 – were in Glasgow for the day.
They visited Kelvingrove Art Gallery and Museum and parked in what looked to them like a regular space.
But when they returned to their car hours later, they had been given a ticket for parking in a "marked" disabled bay without displaying a blue badge.
Mr Fraser took a picture of the bay, which appears to have no clear markings indicating it is reserved for blue badge holders.
Showing the Evening Times the picture, Mrs Fraser said: "Does that look like a marked bay to you?
"We didn't turn up and purposefully park in a disabled bay. I hate when people do that and we would never do it ourselves.
"I was stunned when I read the ticket, so we took a picture and thought the council would admit the mistake and cancel the fine. But it has gone up from the original £60 to £164 because I refused to pay it.
"We would never have parked there if we knew it was for disabled people, but this was not marked.
"I have had the sheriff officers round already, but thankfully we were not in. "
Mrs Fraser, who lives in Falkirk, says she has not been able to state her case to anyone at the council and believes if a senior member of staff at the council's parking department sees the picture, he or she will waive the fine.
She said: "If this was heard in a court of law, the case would be thrown out immediately.
"The council should mark the bay properly to catch people who are abusing the system and not try to squeeze money out of people who had no way of knowing they were doing anything wrong."
The picture appears to show the remnants of paint that at one time marked the bay as a disabled space, but is so badly faded it is no longer clearly marked.
A picture taken four days ago also shows the same unmarked road.
However, the council insists clear signs are attached to poles near the parking bay.
A spokesman said: "The council takes the issue of able-bodied people using bays for the use of disabled drivers seriously.
"These bays have been specifically designated to allow those with mobility problems equal access to visit the museum.
"The markings may have been worn, however the sign next to the parking bay is clear.
"All the necessary paperwork confirming what action would be taken against Mrs Fraser has been sent to her address.
"However, following her initial appeal no contact was made with the council and this has resulted in the escalation of this parking control notice and the outstanding amounts due.
"An independent appeals process is available to any motorist not satisfied with the council's decision."