My daughter's favourite book is
TGC A Coronet for Cathie by Gwendoline Courtney | Girls Gone By Publishers (ggbp.co.uk)
Very much an old fashioned book, but it's one of two books she took for light reading to uni (the other being the very long Les Mis!) I don't think it's made clear what illness Cathy has but the book is about her recovery around a fairly typical 1950s school story theme!
Some of the Famous Five (Five get into a Fix) and at least one of the adventure series (I can only think offhand of The Sea of Adventure, but there might be another) and I think Holiday House is about a house for convalescence, although I might be wrong there. I think at least one of the Faraway Tree sets has a cousin (either Jo or Connie) who comes to them for a rest after being ill, but I might be wrong there.
Susan, Bill and the Wolf Dog, (Malcolm Saville) Susan starts off as having been very ill.
A Storm is Coming by Monica Edwards starts with Lindsey coming to convalesce with Tamsin, and ends with Tamsin recovering from Pneumonia. Also in I think it's Punchbowl Midnight Tamsin has to spend some time convalescing after being shot (not as dramatic as it sounds).
In Further Adventures from One End Street (Eve Garnett) the younger pair (Peggy and Jo) are sent with big sister Kate for convalescence after measles at the Dew Drop Inn. In the following book (Adventures of the Dew Drop Inn) Kate is sent for the same.
I'm sure I have more around just can't think of any at present.
Edited to say: Actually going back to the Noel Streatfield, I think your want for sibling views might work with Apple Bough (I think it's rather badly called Travelling Shoes now), although he isn't ill (mostly) it's got the siblings being dragged round for their genius brother (that they love very much) and could fit in.
White Boots (Skating shoes) is probably her best convalescence story though but it does have her siblings involved.