The family was told by Dudley Council to pay 'top-up' fees or the woman would be moved to a cheaper home.
The authority has apologised and issued a £4,600 refund to the family after the ombudsman ruled they were treated unfairly.
It follows a two-year long row between the authority and the family over the cost of their mother's care.
An investigation found that the family were given 'no alternative but to pay third-party top-up fees' for their mother's care.
The mother, who had vascular dementia, moved into a care home in February 2015 after the family initially agreed to pay £408 a week, including the top-up - money relatives can pay if they require more expensive care than a council is offering.
The move was arranged by the Dudley and Walsall Mental Health Partnership Trust, on behalf of the council
However, social care experts have said families should not be left with the bill just because it is more than a council is willing to pay.
Councils are expected to offer care homes which are affordable if relatives are struggling to pay.
In November 2015, the family said they could no longer afford the £50 weekly fee and asked for the council’s help.
The mother’s needs were reassessed, but there was no record of any consideration of the affordability of the £50 weekly top-up fee, the ombudsman said.
Dudley social services told the family the council would not pay the rest of the top-up fee, but would support the family if they wanted to consider moving their mother.
The family complained to the council but bosses insisted if they could not afford the £50 top-up, then the vulnerable woman would be moved to a cheaper home.
The aggrieved relatives took the case to the LGO, which has ruled in the family's favour.
It concluded the trust, acting on behalf of the council, 'had not acted in line with statutory guidance' when arranging the mother’s care and that there was no evidence any alternative placement was made available for which the mother would not need a top-up.
Michael King, from the LGO, said: “Families can only make proper informed decisions about their relatives’ care if they are given the correct information.
"In this case, the family was only presented with one option - to pay a top-up fee - and no further details about their rights."
Councillor Nicolas Barlow, cabinet member for adult social care at Dudley Council, said: “The Local Government Ombudsman has issued a report about the council’s top-up fee arrangements and has made a number of recommendations, which we accept.
"We will implement these carefully and have already sincerely apologised to the family involved and organised a refund of the top-up fees they have paid to date.
"We are also part way through carrying out a review of our arrangements to ensure we improve the process for service users and their families and to avoid such incidents in the future.”
The woman remains in the home.
The Dudley and Walsall Mental Health Partnership Trust declined to comment.