Lady June has been in a long-running dispute with Sir Ed's children, Peter and Sarah.
Sarah Hillary said last night that internal politics had not directly led to the resignations.
"I couldn't say why they resigned together. June's the only one who has said something, which was she felt that for 50 years she had been doing it for long enough and was proud of what she had done."
The Himalayan Trust, with four council members remaining, issued a statement to the charity's stakeholders thanking the departing members for their work and promising a series of reforms.
Ms Hillary said the statement was meant to reassure. The trust's original constitution would be modernised and updated - a process already started before the resignations, she said.
"It's hard when someone like my father, who was the founder and also able to raise huge funds, dies. What do you do at that point? ... We also need to re-look at the charity's directions."
She hoped attention would now turn away from any disagreements to the work of the charity itself.
"It's had so much support from the New Zealand public. We want to capture that as much as we can ... that enthusiasm that people have and that feeling of closeness with that part of Nepal."
The resignations come after last year's public spat over the ownership of Rolex watches, including one given to Sir Ed after he and Tenzing Norgay scaled Mt Everest in 1953.
Peter and Sarah Hillary blocked Lady June's attempts to sell the watches with court orders and were eventually awarded ownership by the courts.
