Lucy Brown, 40, drove boyfriend Kevin Hall, 34, to Nottingham train station with their 16-month-old son Kit in the back and pulled up in the drop-off zone on 7 June.
Hall took six minutes and 45 seconds changing his son in the back seat before he left, but Brown received a letter a week later informing her she had been fined £70 for parking in the space longer than the permitted two minutes.
Hall said: "I could tell he needed a nappy change so I quickly got in the back of the car to do it and gave him a cuddle before I left. We weren't causing an obstruction or anything like that."
The couple, from Colwick, in Nottingham, have accused "jobsworths" at East Midlands Trains of trapping motorists with the "ludicrous" and "unethical" time limit.
Hall added: "We pulled into the drop-off point thinking it would save us a lot of bother with parking.
"Kit never likes to say goodbye to daddy so he was crying as I got out.
"I didn't realise you're given only two minutes to get in and out. That includes pulling in, finding a space, getting luggage out, saying goodbye and then leaving.
"I'm able-bodied and I struggled to do everything in two minutes, especially with a nappy change, so how are disabled, pregnant or elderly people expected to manage?
"It's unethical to say the least and almost like a trap. There is a tiny sign saying two minutes parking, but nothing about a fine.
"It is ludicrous. Two minutes isn't long enough to even drop-off properly.
"I saw other cars parked up behind us and they were there for just as long as we were.
"So I think most people are unaware of the time limit and certainly the fines. I assume they got tickets too.
"I had to pay the fine as I didn't want to be hauled before a magistrates court. Its the most expensive nappy change I've ever heard of."
Hall had been on his way to Warrington, in Cheshire, for work when his partner's Vauxhall Antara was clocked by the automated cameras.
The couple have twice tried to appeal the penalty but East Midlands Trains (EMT) has rejected their claims they were unaware of the time limit.
Full-time mum Brown, who is two months pregnant, blasted the firm - owned by Stagecoach Group - and accused them of using "bullying" tactics.
She said: "The fact that only recently East Midlands Trains has erected a sign albeit a temporary and not necessarily visible one to the reasonable man just goes to prove how unfounded and cynical their tactics to date have been."
It emerged last month EMT collected a whopping £24,000 in fines from 700 penalties issued to drivers for overstaying.
Shadow Chancellor of the Exchequer Chris Leslie, MP for Nottingham East, said: "While I understand that EMT's traffic enforcement team has to make sure that people are parking appropriately, some common sense needs to be applied.
"A little leeway should be shown where it's obvious that people are stopping very temporarily and may have to deal with something unforeseen, such as stopping to look after children."
A spokesman for East Midlands Trains said: "The two-minute drop-off zone is monitored to prevent congestion and to make sure others can use the area.
"The drop-off zone provides a convenient location to be dropped off near the station.
"For those who might wish to park for slightly longer, there is a completely free 30-minute pick-up and drop-off zone in the station car park immediately next door."