Svenska Akademiens ordbok explains that the word ANNORLUNDA is built of two parts: ANNOR, which is an archaic form of ANNAN, and LUND, which means SÄTT. Here are the links: http://g3.spraakdata.gu.se/saob/show.phtml?filenr=1/13/210.html http://g3.spraakdata.gu.se/saob/show.phtml?filenr=1/13/173.html#ANNOR-LUNDA
Technically, the meaning "alternative" could match ANNORLUNDA, but there already is a word for it in Swedish, it's ALTERNATIV. The word ANNORLUNDA is very very old. To my ear, it's a very basal, uncomplicated, simple word that all country side folk had been using for centuries. It just does not mix up with fancy modern words like "alternative".
I just found out that the synonyms website http://www.synonymer.se/?query=annorlunda hints that UDDA is a synonym to ANNORLUNDA. UDDA is actually "peculiar", so, after all, the disputed translation can be accurate.
The word "peculiar" originally meant "of one's self" so "peculiar to one's self" would have made perfect sense and in this way the sentence is more understandable as in "she chose her own way" as opposed to a clear way already marked out (I suppose this could be figuratively "through life" but also makes sense in a literal form). It's only fairly recently that peculiar has taken on the meaning of odd or strange. C.f. the etymology of "weird" which now has similar connotations but originally meant "fate"
Here's a nice post that explains it. Just scroll down a bit. http://www.thelocal.se/blogs/theswedishteacher/tag/annorlunda/
"different" is only a good translation in its informal use, in which it is used to mean more like "unconventional, abnormal, or unfamiliar". The real definition of different is simply "not the same". I think "peculiar" is a much less ambiguous translation and seems to be the correct match unless *annorlunda" gets abused in the way "different" does making its definition ambiguous. :)