Marie Husbands, 74, was admitted to hospital when her heart valve started to leak. She then contracted MRSA twice, was delayed in getting an intensive care bed and then died days after her operation. Her family believe delays in transferring her from Hairmyres Hospital, in East Kilbride, to the Golden Jubilee, Clydebank, for cardiac surgery may have led to her death last month.
The two health boards have launched a investigation.
Mrs Husband, a grandmother-of-two, who was from Strathaven, Lanarkshire, ad a heart valve replaced in January 2013 but was admitted to Hairmyres Hospital this year after doctors discovered the valve was leaking.
Doctors initially tried to stabilise her medically with drugs, but it became clear this was not working and her condition began to deteriorate.
However, it was more than two months before she was transferred to the Golden Jubilee for heart surgery.
Her family say a number of scheduled meetings that had been set up between doctors at the hospitals to discuss her condition did not take place.
They say the pensioner, who has two sons, Iain, who lives in Glasgow, and Stephen, who lives in Bath, also caught MRSA twice and another delay was caused after an ICU bed she was due to be transferred to was taken up by another patient.
By the time she was transferred for surgery, the family say she was seriously ill and she died last month shortly after the surgery.
Her brother Geoff Caine said the surgeon at the Golden Jubilee was "shocked" at her condition when she arrived at the hospital. Mr Caine, who lives in Manchester, said: "There were several delays in the move to Golden Jubilee for the operation. There were missed meetings, she caught MRSA on two separate occasions and then, finally, the ICU bed she needed was booked for someone else."