Gemma Hodson, whose father-in-law lives at Regent Bay Holiday Park in Westgate, said he'd been left worried and confused by instructions from the park on Tuesday, March 25.
Some reported that the parks had threatened to turn off water and electricity if people did not leave.
Parkdean Resorts, which also runs Ocean Edge Caravan Park in Heysham, said it was a complex situation, but that it was able to make allowances so that people can stay on their parks.
Lancaster City Council said that it had been in touch with Parkdean Resorts to remind the company about government guidance.
This states that if people live permanently in caravan parks or are staying in caravan parks as interim abodes where their primary residence is not available, they may continue to do so.
Gemma said: "My father-in-law and his wife received a letter and went to speak to the manager.
"They have another house which is occupied by his son and his wife, but they are self isolating, and when they explained this they were initially told they could stay on the park.
"Then they came with another letter which said they had to leave immediately and return home.
"They're in their 70s, and they're supposed to be self-isolating.
"It's their main place of residence, and they've paid all their fees for the year so they can live there.
"There are vulnerable people there, and the situation has left people very stressed and anxious, and some have been in tears."
A spokesman for Lancaster City Council said the authority had been in touch with Parkdean Resorts' regional director, and reminded them about the government guidance, which is for people not to move if they have nowhere else to go.
Lancashire County Coun Lizzi Collinge said that people should not be moving.
"We know that a lot of people live there for most of the year," she added.
"What we need to minimise is people moving across the country and spreading this virus.
"People have got to get their head around the fact that the best way is to reduce the spread is to stay put, if you can, or if you have nowhere else to go."
A spokesman for Parkdean Resorts said: "The parks were forced to close following the government's shutdown announcement.
"On Tuesday morning, a letter was sent to holiday home owners, explaining that people would have to leave the parks at their earliest convenience and go to their main residence.
"The letter also said that if people could not do this, they should speak to the manager to discuss whether they are able to stay on the park.
We understand that not everyone can leave, and Parkdean's position is that where people can't go anywhere else, then we can make allowances for people to stay on park.
"The park’s General Manager is handling these situations on a case by case basis. The last thing we want is for people to leave parks with nowhere to go."