Even though 'rest' was very much in vogue in Alexandra's day, fresh air was also very much the thing, at least in Britain, so sitting outside in the fresh air was frequently prescribed, along with going away to milder climates where one could sit outside in winter.
I quite accept that when in the grip of depression the temptation is to hide yourself away, but there comes a point when one has to steel oneself and make an effort to stop doing that. Alexandra, for all her protestations that she did not want to burden her husband and daughters, did burden them - all the business of one of the girls being constantly with her, for example. There is a theory that there comes a point when family patience etc becomes counter-productive, because it allows the afflicted individual person to carry on doing what they are doing with absolutely no incentive to help themselves. This is most obviously applicable to alcoholics (who quite often have endlessly patient wives or husbands who prevent them from having to face up to the consequences of their actions). It is called co-dependency, I think.
Ann