TL;DR: I can not leave my job right away, how to handle a situation where my manager is more lenient towards his favourite while maintaining (wittingly or unwittingly) a different array of expectations and rules for me.
There is a saying, keep your friends close but your enemies closer.
A strategy others have not suggested thus far that might work: try to make friends with the 'favorite'. NO!!! Not the favorite! Of course, don't be mean to the favorite, but don't bend over backwards to befriend them either. Instead, try to make friends with the Manager.
This doesn't mean suck up and denigrate yourself. But it does mean try to be helpful in ways that make their work easier.
Maybe offer to take some tasks off the manager's plate if he gets overwhelmed. Maybe offer to take on some coordination/liaison tasks or help facilitate some meetings to save the manager time and effort. Maybe build some strategic connections across other teams and offices that provide an advantage to your team in terms of helping improve communication and make the work flow more smoothly. Observe carefully your manager's work and try to identify some of the 'pain points' that cause issues or challenges for your manager, and think of anything you can do to help address those.
Focus your effort on supporting the work of the team and the work of your manager. Unless your manager is an idiot, it will not go unnoticed. Don't be too "proactive" about this, but a little more subtle. First observe, and then try this or that approach and see what 'sticks'. If something doesn't work, don't try to argue your case, just back away. Listen to your manager's feedback, don't disagree, be adaptable and flexible but keep looking for ways to be of help and improve the quality of the team's output.
Managers value it when staff (a) don't cause them problems, i.e. are not troublemakers and (b) do their fair share and then some, are reliable performers who help push the envelope on the main projects the team is tasked with.
Become an 'asset' and someone that the Manager has a vested interest in keeping on his good side. The 'favorite' situation might not go away completely, and you might never quite reach same status. But you will still be valuable enough that the manager will feel compelled to protect you and defend you in case the 'favorite' gets out of hand. At a minimum, you will earn yourself some points that will allow you to request (and obtain) the flexibility where you need it, similar to what the favorite may be getting now.
True, you'll have to work a little harder to get to the same place, but life is unfair. What counts is that you will get there. Over time, your manager might begin to realize who should be the real favorite, and why. Good luck!
There is no real solution apart from leaving, only a number of hard options:
In a sense, your options are defined by how "professional" your company is about such things. Even if they have a framework in place to deal with such behaviour, it is likely to entail quite a high burden of proof, which can be impossible to come by.
There is no way to make your life a little better, as you have to go to work as long as you are employed there, and therefore will keep interacting with your colleagues. Although you can try to reduce interaction (eg by working from home), it usually doesn't work very well.
You could try an internal transfer.
The hardest option, which could also blow up, and could be very hurtful to you: speak to both the manager and his favorite directly about this. Don't forget however it is likely a zero-sum game: the favorite has everything to lose, and nothing to gain admitting his status. On the other hand, the manager may have something to gain from you not creating too much fuss if your fuss is likely to reflect badly on him. In return for that, you may be able to get the manager to change the setup slightly.
You need a new job.
But since you can't leave your job, you'll just have to suck it up, lay low and don't stir up shit, won't you...
The only conversations I get invited to are the ones where the critical decisions have already been made.
Unless you're a team lead, this is quite normal.
my visa has not been processed (work hasn't sponsored me but I can't have instability).
If your visa has not been processed you have no visa thus are working ILLEGALLY !
Seek immigration advice from a lawyer immediately.
You can only start working once you have a valid official visa.
You said you work there for 2 years and your visa has still not been processed?!
Either I'm misunderstanding or you're in serious trouble.
Also, also: Your question is TL;DR !