The Firth Park Friday Club, in Sheffield, has visited Butlins in Skegness for the past 19 years but this year the manager has refused admission.
Butlins said it found "large all-adult groups very intimidating".
Christina Staniland, 86, whose son travels with the club, said the group were "heartbroken" and "angry".
Mrs Staniland, of Longley, said 26 adults and a group of 10 carers from the Friday Club had visited Butlins for a number of years.'Cried a lot'
However, when the group attempted to book this year's break, they were told large groups were only accepted "at the resort director's discretion".
Mrs Staniland's son Gary, 59, has Down's Syndrome and relies on day and respite care.
She said: "I'm more than angry. I've cried a lot myself. I'm not only fighting for this but to keep the day services and the respite care."
Butlins said in a statement that due to the group size "growing in recent years" it was "unable to accept this group unless they come in two smaller groups on different breaks".
"We are concerned that a group of adults has experienced some inconvenience over a booking they attempted to make through a travel agent," the company said.
"Unfortunately the group has not been in direct contact with us to discuss the situation, but we would welcome the chance to speak with them and resolve this.
"We do not generally accept large all-adult parties during family holiday breaks. In this particular case the party consisted of 36 adults.
"We would be more than delighted to welcome this group if they can be split into two parties on different breaks."
Mrs Staniland said breaking the holiday into two groups on separate dates was not an option as the council funding was only for a certain date.
She said the decision was "shocking" and she could not understand the resort's decision as the group had not received any complaints in the past.