"...the reception of Carlota in Europe was icy at best, even by her own brothers Leopold II and Philippe during her 10-month sojourn in Brussels. Her reputation for eccentricity - bordering on mad paranoia - preceded her even in the courts of Europe, and King Leopold himself saw to it that Prince Louis Maximilian spent substantial time with his uncles and cousin, the future Leopold III [1], to "avoid her mutterings and musings." (By modern standards, the treatment of Carlota by her contemporaries obviously has substantial whiffs of sexism, of dismissals of a woman due to her gender, but it is still likely that Carlota did suffer from some adverse mental health issues, most likely severe depression. Her beloved husband's frequent dalliances, of which she was often aware, affected her deeply). The extended, nearly three-year time Carlota was in Europe, coincidentally and conveniently corresponding with the revolts stared down by her husband at home, was not just to expose the Crown Prince to a European education but also to tour the continent seeking out an appropriate bride, and ideally bring her home to Mexico to assimilate to the country before her son's majority. Carlota's eye was first and foremost on her niece, Clementine, whom she entertained and aggressively tried to woo. Leopold was neutral to the match, and indeed Clementine would eventually marry her cousin Baudoin [2], but her mother Queen Henriette was aggressively opposed, having come to detest Carlota during her stay. It did not help that the Belgian royal family did not care much for Louis Maximilian, who by this point a late teen-ager began to show some of his later personality traits - a mercurial temper, a contempt for household staff, and bouts of depression and paralyzing terror. Dismissed in his day as merely having inherited his mother's madness, it is quite likely in hindsight that the Crown Prince would suffer from post-traumatic stress disorder his entire life, thanks in large part to the severe injury sustained to his face, causing the loss of his left eye, much of his left ear, and the permanent scarring of his temple and side of his head, on the attempted assassination on the day of his first communion.
Carlota departed Brussels shortly after the marriage of her nephew Prince Leopld, the Duke of Brabant, to Marie Anne of Portugal in early 1883 [3]. Her destination was Vienna, where she wanted Louis Maximilian to spend time with his uncle Franz Josef, learning the history of his father's land and picking up matters of Court. It was here in his nearly two years in Vienna that Louis Maximilian, all of 15 upon arriving, developed his penchant for prostitutes, being taken under the wing of the infamous Crown Prince Rudolf, his cousin. (Leopold of Belgium, it should be noted, was infamous for his extramarital affairs as well, but never once thought to drag his young cousin out to get him into any sort of trouble). Carlota also saw the stay in Vienna as an opportunity to "find a Habsburg girl" for her son to marry, after her embarrassing failure in Brussels. The Empress' eye fell on Archduchess Valerie (full name Marie Valerie), Franz Josef's youngest daughter, who was almost precisely of an age with her son down to a few weeks and was famed for her beauty (and remarkable resemblance to her father, contrary to rumors of her parentage). Once more, she was defeated by the desires of the girl's mother - while "Sisi," the Empress Elisabeth, did not loathe Carlota in the way Queen Henriette did, she loved Valerie above all her other children and was firm that her favorite daughter would not have to marry against her will. Franz Josef, despite seeing the match as favorable, especially as Louis Maximilian came to be extremely smitten with his cousin, was unable to overrule his wife in this matter, as with most matters in their unusual and tumultuous marriage [4]. Carlota did not press the matter once Franz Josef reluctantly declined her proposal, and Louis Maximilian was heartbroken - the Crown Prince would never fully reconcile himself to his Austrian heritage for the rest of his life, taking considerably more interest in Belgian (and French) matters as he grew older and by the time of middle age considering Europe totally alien, and regarding himself as fully Mexican [5], which neither of his parents ever did.
The saying of course is that the third time is the charm, and Carlota did find her husband his future wife during their time in Vienna - the third daughter of Archduke Josef Karl, Palatine of Hungary, an archduchess two years Louis Maximilian's junior by name of Margarethe Klementine. From the Hungarian branch of the Habsburg line, it was an almost insultingly junior match for the future Emperor, and Louis Maximilian even at 16 found her plain when in late 1884 his mother introduced them at a ball in Budapest. Nevertheless, Josef Karl and his wife were much more amenable to the match than Carlota's brother or brother-in-law had been, and the Archduchess' minor noble German mother did not protest. Shortly before returning to Mexico in 1885, the engagement was announced, and Carlota made arrangements for the future Empress Margareta Clementina - who would be one of the Mexico's most famous public figures in time [6] - to journey back to join her family in Chapultepec and learn to "become a Mexican" before she was married to her betrothed..."
- Maximilian of Mexico
[1] In this TL did not fall in a pond and die
[2] Who here survives, of course, not that it will have a huge impact outside of Clementine not marrying Prince Victor Napoleon
[3] Marie Anne still winding up marrying into a Catholic Low Country monarchy, albeit a decade earlier in Belgium rather than William of Luxembourg... who we will be keeping an eye on. Stay tuned.
[4] Franz Josef was totally devoted to Sisi, who really didn't care for him
[5] Probably for the best, of course
[6] This chapter of course jumps around chronologically a bit, with some minor flashforwards. Of course, a big one here is an obscure minor Habsburg archduchess becoming a major future figure in Mexican history, which is part of what makes projects like this so fun. It took a LOT of work for me to find Louis Maximilian an appropriate bride, I'll just leave it at that (the two failed marriage proposals basically match up with me going "hey this one could work! Err.... maybe not")