not exactly. The spearhead of the "movement" against Juan was both his stepmom, the Princess of Beira, and his archreactionary wife, Maria Beatrice d'Este, who had the custody of his kids. Essentially what happened was that the radical conservative arch-Catholic reactionary fringe of the party muscled out anyone who tried to breathe in some moderation, regardless of who they were or devotion to the cause (Beira even disowned her own son, Infante Sebastiao, when he advocated they make peace with the Isabellinos; when the pope peaced out with the Spanish government, likewise the pope was disowned).
Also, they neither declared Juan illegitimate- since that would've been a snake eating its tail, given that he was the only Carlist heir with children and his wife had no claim to the Spanish throne- nor "threw him out" in favour of his reactionary brother. He was persuaded to "abdicate" in favour of his son when he realized how polarized things had become and that most of the party wouldn't accept him as their candidate for the Spanish throne after Isabel II was deposed. His brothers were both dead by this time, and it's telling that his so-called ultra-reactionary son, once he was in power, managed to purge a lot of the ultramontanes (many of whom were the same ones who refused to accept the abdication as valid, despite their dislike of Juan) from the party. This included the "kingmaker" who had recommended that Juan abdicate in Carlos' favour. He at least made a convincing show of attempting to attract liberal politicians to the party. He didn't promise them anything or capitulate- he veiled everything under "if I'm restored I'll do xyz"- but remained suitably nebulous about how or when he would go about his policy. There was some enthusiasm for him- see that the Third Carlist War was probably the closest they'd ever gotten to an actual win; or that, when they were scouting for candidates, he was more popular than both the duque de Seville (who was hated by anyone not a socialist) and the duc de Montpensier (who was hated by pretty much all Spaniards), not to mention the other ideas of "importing a king" (either choosing Fernando II of Portugal or choosing one of the Bavarian sons of Infanta Amelia). He had a wife who was popular in Spain, he toned down the reactionary rhetoric and he had a son and heir (born a mere two days after Isabel II abdicated).
this is an unfair criticism of the Carlist cause- same for the Légitimist cause- by their liberal opponents. Re: légitimism in France, Henri de Chambord had far more in common with Napoléon III's regime than Louis Philippe's. Same for Juan. Don Carlos "abdicated" his rights to his son in Bourges in 1846. Most of the ultramontane side that refused to accept the abdication as valid stayed with the count of Molina until his death in 1851. So, in short, between 1846-1851, that's probably the moment to strike. They will no doubt insist that he leave those ultramontanes in Trieste with his father (meaning those that return with him are those that are the "moderates" and the "liberals" in the Carlist party, willing to make their peace with the Isabellino regime). When his father dies, those ultramontanes can object to accepting him as king of Spain, but to do that, they would have to betray the very principles which led them to associating with the Carlists in the first place (legitimacy, anti-liberalism and so on). Same goes for them accepting the son and not the father.
