I have found two sources that state that Helen, Duchess of Albany and her children Alice and Charles had use of Birkhill from the 1880s onwards! Whether QV gave Birkhall to Leopold and Helen is not certain or perhaps QV gave the house to the widowed Helen!? Anyway, I do not know if Helen retained use of the house up until her death although it would work neatly on a timescale if she did, as she died in 1922 and the next known occupants Albert Duke of York and his wife Elizabeth married in the following year.
Apparently Birkhall was originally purchased as a home for Albert Edward, Prince of Wales and his family! But for some reason he seems to have preferred Abergeldie Castle which was leased from the Gordon family, and after he and Alexandra moved into Balmoral the castle leasehold passed to George and Mary to provide them with a 'pad' in the Highlands!