I think you’re thinking of Diana’s family in terms of a ‘normal’, non-dysfunctional, non-aristo one, though. I mean, not alone was her father reputedly violent to her mother (who’d married at 18) and was granted full custody when her mother left him for another man, but her mother then didn’t live nearby to see as much as she could of the children she divided her time mostly between a Scottish island and a sheep farm in Australia, divorced again, and was banned from driving after drink driving, and seems to have had a quarrelsome relationship with Diana.
That kind of childhood environment can often drive children apart, especially once you add in a hated new step parent, because they just don’t have enough energy to do anything more than focus on their own survival.
And add in a household where all the children were sent to boarding school very young (Diana was nine), and I think you have a situation where the relationship is already much more distant than when you grow up together all the time. At four and six years older, she may not have known them all that well before they started boarding, especially as I think she and Charles lived with their mother for a while after the separation.
Then if you add in the complications that one sister introduced her to the man she would have a disastrously unhappy marriage to, after she’d had the good sense not to marry him herself, and the other was married to the queen’s private secretary who represented the Palace’s ‘grey men’ she hated so much, I’d say you don’t have a recipe for any kind of normally supportive sisterly relationship, though Sarah McC travelled with her sometimes as unofficial lady in waiting.