Detectives are investigating a theory that Valerie Graves, 55, who owned a home near Jedburgh, Borders, was killed during a possible break-in at the waterside property in Bosham, near Chichester, West Sussex.
Police hunting the murderer of the mother of two grown-up children were also delving into her past for clues after the discovery of her body on Monday morning.
Officers appealed to anyone who saw someone with blood-stained clothes or who has been asked to wash or dispose of clothing in unusual circumstances to come forward.
The appeal came at a news conference where Ms Graves's son, Tim Wood, sat by his sister, Jemima Harrison, to pay tribute and call for information.
Mr Wood said: "My mum was much loved and will be sorely missed by the whole family. She was a free spirit who enjoyed her life and was a talented artist.
"She had lived in Scotland for about 10 years, a place she loved and which inspired her passion for art."
He said that his mother's death had been "devastating for the family". He added: "We would appeal to anyone who has any information about this, no matter how trivial it is, to contact the police to help us catch whoever has done this horrible act."
Ms Graves, who had a cottage in the Borders hamlet of Maxton, was house-sitting at the property with her mother, sister and her sister's partner while the owners holidayed abroad.
Detective Superintendent Nick May, of Sussex Police, said she had arrived just before Christmas.
Ms Graves, who had recently moved back to Sussex from Scotland to be closer to her family, went to bed at 10pm on December 29. She was found dead by one of her three relatives at around 10am the following day in the bedroom where she had been sleeping. It was not revealed whether she was in bed at the time.
A post-mortem examination revealed she had suffered significant head and facial injuries, but Mr May did not confirm whether a weapon had been used.
The death has shocked the small community of Bosham, which has previously featured in an episode of the ITV crime drama Midsomer Murders.
No arrests have been made, but Mr May said significant resources were being deployed involving detectives from across Sussex and Surrey.
Asked about any recent threats against Ms Graves, Mr May said: "We are doing an awful lot of work trying to understand about Valerie's life, who she associates with and who may be connected in that way."
Mr May declined to reveal whether there had been any signs of a break-in or whether any items had been stolen from the house.
He added: "We have not nominated any suspects in this investigation and we are pursuing a large number of lines of inquiry."
The owners of the house, listed on the electoral register as Malcolm, 66, and Caroline Chamberlain, 63, were still abroad and were "fully co-operating" with police.
Asked how they were dealing with the murder, Mr May said: "They are extremely shocked by what's happened.
"They are horrified, as you can imagine.
"They are being absolutely supportive of the police investigation.
"One of the lines of inquiry is that this act has been committed by somebody unconnected to Valerie, and yes, that is a possibility.