RSPCA officers found the pets in 'appalling' conditions when they raided the house in Sedgley, magistrates were told.
Two German shepherds and two German shepherd husky crosses were kept outside in pens filled with urine and faeces and at the time had no access to water.
A Jack Russell called Honey, who lived inside the house, on Turls Street, was found to have gnawed away at a tumour and had not been taken to the vets.
When the dog was rescued it was decided she was in such a bad condition she should be put to sleep.
Owners David and Diane Roberts, and Diane's daughter Naomi Heydon, admitted nine charges each relating to causing unnecessary suffering to animals and failing to meet their needs at Birmingham Magistrates Court.
Mr Rafe Turner, prosecuting on behalf of the RSPCA, told how the dogs suffered with a range of problems, including dental disease, ear infections, and skin conditions.
On a scale of one to nine, with one being emaciated, one of the dogs scored two and another 2.5, Mr Turner said.
Mr Turner said: "At the time of intervention there was no evidence the dogs (outside) had access to fresh water.
"They weren't able to display normal behaviour patterns simply because they were kept for so long in these pens.
"They were not taken out on a regular basis for exercise.
"Six dogs were neglected in various ways. They were kept in appalling conditions. Four were kept outside in squalid conditions."
When questioned, Mrs Roberts, aged 52, said the dogs in the pens were mostly the responsibility of her husband as she struggled to get outside due to mobility problems and the 'decking was slippy'.
Mr Roberts said he let the dogs out for 15 minutes a day and said the dogs weren't taken to the vets because it was 'too expensive'.
Heydon, 25, who owned Honey, claimed she was 'going to do something about it' but that the RSPCA came before she could.
Mr Turner said: "It is quite obvious the dogs should have received veterinary care.
"The environment was wholly unsuitable and sadly one dog had to be put to sleep.
The three are due to be sentenced on May 31.