A 92-year-old woman spent 11 hours on the floor of her home waiting for an ambulance before spending another 16 hours in the vehicle, her family say.
Dona Beynon, from Pontyates, Carmarthenshire, also caught Covid while in Withybush Hospital.
Her family said Mrs Beynon was shown a lack of respect and dignity in hospital before she died in April.
Hywel Dda health board and the Welsh Ambulance Service said they were sorry to hear about Mrs Beynon's experiences.
Mrs Beynon's family want answers from the health board and the ambulance service over what they called "neglectful treatment" of their mother, who had a cut head and broken arm while waiting on the floor for the ambulance.
Her daughter, Elsbeth Jones, said the wait in an ambulance was outside Glangwili Hospital in Carmarthen before she was transferred to Withybush in Haverfordwest, 30 miles (50km) away.
Mrs Jones said the family were not given any means of contacting Mrs Beynon for 10 days after she contracted Covid and had to "wait hours for answers".
"When we saw her at the end of this it was quite horrendous. She looked a shadow of her former self and she had a haunted look in her eyes," she added.
When Mrs Beynon arrived at Withybush on 14 March, the family said she was lucid and clear thinking but was considered "confused" by staff on duty that night because she spoke Welsh - her first language.
She died on 5 April, a few days after the family took her home.
Mrs Jones said: "I think it is important that other people are not treated in the same way.
"It is quite, quite disgusting and I would hate to think how many other older people who maybe don't have families to fight for them have been through this experience and go through it today and will in the future if nothing is done about it."
The family has also contacted Welsh ambulance service chief executive Jason Killens, calling for a "more humane way of coding the circumstances" for each 999 call as "one size does not fit all".
They also said they wanted an "honest explanation in answer to the sad sequence of events" that led to their mother's death.
Mandy Rayani, executive director of nursing, quality and patient experience at Hywel Dda, said: "While we are unable to comment on individual patient cases, we are always sorry to hear of any instance where patients feel they have not received an appropriate standard of care.
"We would encourage anyone who has a concern regarding the treatment or service they receive to contact our patient support team."
Wendy Herbert, the Welsh ambulance service's executive director of quality and nursing, added: "We wish to send our sincere condolences to the family and we are deeply sorry to hear about their experience, which we understand would have been distressing.
"Demand on our ambulance service remains high and this, coupled with excessive hospital handover delays, means that some patients in the community are having a very long wait for our help, potentially many hours in times of extreme demand."