The family of Scotland international Siobhan Cattigan are calling for an independent inquiry into the circumstances that led to her death.
The family say undetected rugby-related brain damage caused a "catastrophic decline" in the 26-year-old's health and resulted in her death in November.
They say she was not given the required assistance for brain injuries.
Scottish Rugby has been contacted for comment but said recently it would not support an external inquiry.
The union has said that court may be "the most appropriate" place to discover the facts.
However, the Cattigan family, who have launched legal action against Scottish Rugby and World Rugby, said in a statement: "As a family grieving for our beloved Siobhan, we have been shocked and distressed by the recent actions of the SRU.
"We cannot understand why the SRU are resisting an independent inquiry into the circumstances leading up to Siobhan's death. We believe this is the best way for the facts to emerge."
Their statement added that the family feel Scottish Rugby's treatment of them has been "callous and uncaring" since the death of Cattigan, who won 19 caps between 2018 and 2021.
"No one from the SRU has been in direct contact with us since February, and the organisation is now taking active steps to discredit our version of events," they added.
At their annual meeting on 13 August, Scottish Rugby officials spoke of the "heartbreaking" story and "extremely disturbing" account from the Cattigans, who had told the Sunday Times they noticed a significant and alarming change in their daughter's personality following brain injuries suffered while representing Scotland.
The governing body said it is engaging in an internal fact discovery process and that there was a limit to what it could say publicly, because of impending legal action from the family against the SRU,
Chairman John Jeffrey remarked that he was "comfortable with the actions of our people", while adding a hope that "in time, the full story will come out".