Bare basics:
Only daughter (and only other child) of William I and Augusta
Married Grand Duke Frederick 'Fritz' of Baden very happily and they celebrated their 'Silberhochziet' (50th anniversary)
Relations (at least in the beginning were very good) but often soured over matchmaking. Louise apparently wanted to be consulted in some of the potential wives for the Prince of Wales (as it was assumed she be German). She had hopes that her brother-in-law William would marry Princess Alice but Vicky recommended against it to QV as she didn't find him very promising. Her son was the potential prince put forward by Empress Augusta to Elizabeth of Hesse who rejected him thus antagonizing both women. (QV referred to him as 'good Fritz Baden' and hoped Ella would accept him--he later married Hilda of Nassau). They were also irritated that he wasn't considered for Irene. QV blamed Louise and Fritz (Sr) for hurrying on and pressuring Louis & Ella. This caused some discord between Vicky and Louis as she thought he showed 'a want of openness' on this issue. A major beach occured over Sandra & Moretta as Louise was in the camp which opposed the match.
They also quarreled over Countess Blucher. Vicky wanted her as part of her court as she was a 'Baron [Stockmar] in petticoats' and capable of standing up for them. She was very in line with Vicky's view on the world and she was 'a Prussian and an Englishwoman'. Louise wanted her too and says she should be at her court because she lived at Baden.
Vicky expressed the view that in light of the constant (and acrimonious) bickering between William & Augusta that she was glad that Louise lived far enough away that she didn't have to bear witness anymore to the upsetting scenes the way she and Fritz did.
Was much beloved in Baden for her many charitable endeavors, especially Red Cross work during WW1 despite her advanced age.
When Sophie apparently compared the length of her mother's letters and the habit of peppering them with questions designed to elicit lengthy replies Vicky responds:
'I am much flattered to be compared to Aunt Louise of Baden! The difference, you see, is that _she_ asks questions because it is a habit and she cannot help it, because it is her way of making conversation, and because she loves meddling in other people's affairs and making herself important. I do not quite think that _my_ reasons are the same!'
Was apparently pretty unkind and unsympathetic to Vicky during Fritz's illness and much in the camp of William and close to Dona.
Vicky lamented that (her) Fritz and Louise weren't closer as they were each other's only sibling and should've been brought closer together by their parents' bad behavior but instead it seems to have made them unable to express their feelings openly to each other. Vicky compared this to her own close (if occassionally bickering) relationship with her own siblings.