Alice had a much better position that her sister in Berlin - because when she arrived in Darmstadt the Grand Duchess had just died and the Princess became in a way the first Lady from the very beginning. That way she was able to do much that Vicky had to fight for - being surrounded by a number of elder princesses and the Queen.
There was another English Princess to marry a Hesse: Elizabeth daughter of George III and therefore Alice's grand aunt became Landgravine of Hesse-Homburg.
The Austro-Prussian War lasted only for a couple of weeks and although Hesse had to pay a huge sum and suffered a lot the Grand Duchy remained independant - and it never strained the sisters relations. Quite the contrary was the case and Alice was quite pro-Prussian. When her son was born she asked Wilhelm I to be one of the godfathers.
that war did definitely not "hurry her to an early grave"
Alice had some intellectual input in Darmstadt - she formed close friendships with extraordinary artists and heads like Louise Büchner, Friedrich D. Strauss, Henriette Sontag, she met Brahms etc...
And as for the "enlightened background" of Prince Albert's: you know that his mother left her children when he was a toddler, that his father and brother were not "gentlemen" in the sence Albert that Albert was.... to say the least. I think on the contrary that he had to fight immensely for his education and compensated his longings for love and affection with learing.
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