King Jérôme spent much in terms of money in his exile, and that caused him trouble in marriage, but in the end, by the time of the Second Republic, the father and the son had been reconciled. Plus, it's unlikely he would be that politically active: he resigned his presidency of the Senate, actually more an honorific office, to protest against Napoléon III and the establishment denigration of his son. Given he was old and probably not physically fit for official duties, I imagine he would have renounced the regency to pass it on his son.
As for Morny, he was for sure a great schemer, and though a half-brother to Napoléon III, he was out of the succession line (due to his bastard status, he was not a Bonaparte per se). His loyalties, through blood ties, would lie in the Bonaparte dynasty without a doubt, but though he is more connected and appreciated than his cousin Prince Napoléon, his task would be nonetheless very hard since the Imperial regime legitimacy much lied in the persona of Napoléon III himself. With the Emperor gone, the velleities of the nominally allied establishment are to be put in test, especially with high temptations of Orleanist restoration (as per the plan stopped short by the coup in 1851). It remains right to say an alliance of Prince Napoléon with Morny will be necessary and in order if there is to be any serious attempt at keeping the dynasty on the throne. This is especially more of a possibility when we know that IOTL, in spite of some dislike between the two, they eventually came close to forming a political alliance before Morny suddenly died in 1865. But for the time being, the perspective of any political reform is to be pushed back to the majority of Napoléon IV due to the problems I mentionned in my previous post, namely the inertia of the political and business establishment. For these same reasons, there is to exclude any major foreign commitment, ie Italy and Mexico, possibly China, though it could keep continuing on minor colonial ventures in Africa mainly.
As far as it matter Prince Napoléon himself, his liberal (and libertine) character and history makes him more likely of sympathies with the British, Piedmont and Italian revolutionaries (though the Corsican he remains in heart is not someone who will forgive easily his cousin's assassination). His rejection of established order excludes Prussia, and Austria to a certain degree, while he holds a grudge against the Church and is a virulent anticlerical (that puts him in Piedmontese side against Austria and the Pope, and through proxy in French politics, the entire conservative wing). But anyway, to repeat my previous argument, the state of political paralysis that would happen in Napoléon IV's minority not only pushes back the perspective of intervention in Italy (and unification which, at the exception of Republicans, is opposed by most of the political spectrum), but it also ends for now Napoléon III's attempted come back of France into European politics (in this, the Italian war played a crucial role), and you would have to wait Napoléon IV's majority to potentially see another comeback.
To make a notice on Prince Napoléon marriage to Marie-Clotilde of Savoy, it wasn't a happy one on account of the contrast between the two, Prince Napoléon being libertine, a womanizer and anti clerica, while his wife, not to mention the big difference of ages, was a devout woman. The marriage was very political and barely accepted by the bride's father (Prince Napoléon's libertine reputation was widely known). I have not in mind a particular bride that could replace her, but I think it's worth to mention he remained in genuine love for his cousin Sophia even though she married the Crown Prince and future King of Netherlands, and the two kept a sustained correspondence (but there was no affair).