Kim Eacott's terrier, Scally, had "separation anxiety" and would bark constantly at her Hereford cottage.
Angela Waring, of Crickhowell, Powys, was held jointly responsible by a judge in the noise nuisance complaint as she owned the home.
She has contested the decision at London's Appeal Court, which will make a ruling at a later date.
Mrs Waring paid for her daughter's cottage despite the pair having fallen out.
The court heard Scally barked incessantly when Miss Eacott was not at home in 2011 and 2012, prompting neighbours Bryn and Diane Cocking to file a claim the noise was "unreasonable in its frequency and duration".
Mrs Waring said she offered to take Scally to a "dog whisperer" to try to calm him down, despite not being on speaking terms with her daughter.
In Worcester County Court in 2013, judge Daniel Pearce-Higgins upheld the Cockings' noise nuisance claim.
Miss Eacott was ordered to pay £3,500 in damages and her mother £1,000. Both were hit with a £31,000 legal costs bill.
Mrs Waring has asked the court to rule that she was not responsible for her daughter, so should not have to pay for her failing to control Scally.
Hamish MacBean, for Mrs Waring, said she had done her best to defuse the row and wrote to her daughter, telling her: "If Scally barks when you are not there, there is a dog whisperer in Abergavenny who can cure him in a gentle way."
The court heard their relationship was so strained Mrs Waring had been advised by police not to talk to her daughter following a harassment complaint.
Catherine Doran, for the Cockings, said: "Were it not for Mrs Waring's failure to abate the nuisance, Mr and Mrs Cocking would not have had to issue a claim at all."
Lady Justice Arden argued Mrs Waring had "turned a blind eye" to the problem.
The court heard Scally has since been put down.
Appeal Court judges reserved their decision until an unspecified future date.

Rescue officials said Minor Vidal, 35, was found with head injuries away from the site of Tuesday's crash.
Mr Vidal told his rescuers he escaped after being trapped in the wreckage and survived by drinking his own urine and water from a lagoon.
Eight people were killed in the crash near Trinidad, in north-east Bolivia.
The Aerocon Airlines flight was travelling from Santa Cruz to Trinidad when air traffic controllers lost track of it. All nine passengers and crew were originally reported to have been killed in the crash.
The head of the rescue mission, Captain David Bustos, said they began searching further away from the wreckage when they found only eight bodies at the crash site.
"From several kilometres (miles) away, we saw a man on the river bank signalling to us. When we got closer, he knelt down and thanked God," Capt Bustos said.
"He said he'd been trapped in the plane for more than 15 hours and that when he finally escaped he began to walk and survived by drinking his own urine and water from a lagoon," Reuters quoted Capt Bustos as saying.
A woman is fighting a £30,000 legal bill after her daughter's yapping dog prompted legal action by neighbours.
[NEXT_CONCEPT]
A Bolivian man who was the sole survivor of a plane crash has been found alive in the Amazon jungle three days after the plane went down.