I would suggest braiding your divergent story lines together as a general principle, but your situation has some special considerations.
In addition, this is my first time when literally every player
provided me with abundance of plot hooks, many of which are quite
divergent. Because of this there's quite a lot of inter-party conflict
and at least two players basically created very apathetic characters,
interested ONLY in their own personal plotline, and can't really
justify why are their characters travelling with the party. This
creates a very strange dynamic. While we all enjoy inter-party
conflicts a lot (even though D&D is in principle a team game), I'm
afraid that in the long run it may majorly derail the campaign.
It seems that your problem characters bring some substantial benefit to the table, while simultaneously being a bane of your attempts at organizing an inclusive character-driven plot. The conflict they provide must be fun on some level, and perhaps the cynical lens through which they view your fantasy world and its heroes provides a compelling counterpoint to your other characters. Their players are roleplaying them true-to-form, which means their motivations don't co-align.
It's up to you to make that happen, and you have a few options. You can try to adjust your players' play style with an out-of-game plea, or you can try to craft your personal plot hooks in a way that encourages them to be cooperative. From the way you frame your issue, I think you might prefer the latter.
Their most powerful general motivations are probably going to be ones of self interest: greed, lust for power, vanity, pride. If the characters have an obsession or a weakness, tweak that where possible. Try to involve these motivations even when their specific goals are not being addressed.
But with regards to specific goals, since these are your most difficult characters to motivate, and they are the least likely to follow the rest of the group, you need to motivate them first and compellingly in order to have a chance to forge the camaraderie that binds the party together. Provide a quest hook that uses that character's background, serves that character's self interest and helps achieve a personal goal, but that simultaneously is compatible with the moralities and priorities of the heroic characters.
Revenge can be an excellent theme for this. A difficult-to-motivate character encounters an opportunity to thwart an old enemy in a painful way, enriching himself in the process, and it just so happens that the target is outright villainous, and is engaged in activities that the heroic characters find very difficult to ignore. Drop in a thread of one of the other characters' story lines so that advancing the one also advances another. Maybe the villain happens to have a clue relevant to another character's personal plot, and can provide a segue that motivates the difficult character to go along.
Hero: Why these letters show that the magistrate is in possession of the stolen finger bones of Saint Jarvis the Emancipator, and that he plans to sell them to Thayvian slave traders! The meeting for the sale is in three days! We must stop this sacrilege!
Not Hero: What's in it for me?
Hero: I just helped you dispatch your tormentor's lieutenant, and I'll swear to help you find your kidnapped sister. Plus, returning the finger bones comes with hefty reward.
Not Hero: Done and done!
While focusing on the difficult characters, ensure that the quest engages the specialties of as many characters as possible so that the other players feel that their presence is worthwhile. This also helps build loyalty. If a difficult character has to rely heavily on the other characters to accomplish his own goals, then he may become more cooperative out of gratitude or a sense of continuing reliance.
While focusing on the other characters, give the difficult ones the opportunity to be self-importantly excellent. Showering them with adoration from the grateful masses in exchange for their reluctantly heroic deeds, building unexpected renown as a valiant protector of the people, can be an excellent motivator for further heroism. It can also come with some serious downsides for a character with enemies in high places.
Give your difficult characters some substantial gains. Let them have their victories. Then, if you want to compellingly tie them in to advancing the other characters' plot lines, threaten to take it away unless they act swiftly and decisively. Self interest works in both directions, and threatening it can really make a player squirm. If it's hard-won organizational prestige, then have that be threatened by a corrupting influence within the organization from another player's adversary. Perhaps the difficult character suddenly finds himself framed for a crime and all of his allies (except of course for the party, who know he's innocent) suddenly become his pursuers, with the puppet strings leading back to a well-established foe that sees the difficult character's new prestige as an opportunity to create a potent distraction.
The plots don't all need to link in, but you should try to tie in one or two other characters each time you focus on advancing a plot that spotlights one character, and hopefully the other players will find opportunities to shine along the way. Like braiding individual strands together, you only grasp a few a time, and slowly you make a nice strong rope.
Then you yank the threads rudely in different directions and see what happens. Does it all unravel, or somehow stay together?