This can be done in a number of ways, but it may affect the plot to your story depending on which you choose.
1. They don't know it's their brother
This one is pretty straightforward. Either they are working freelance to save "someone", (perhaps they know it's royalty that they are rescuing, but have been told no more than that) and when it is revealed that it is the Prince that they are rescuing, the reveal comes that it is their brother.
The advantage of this is that the reader has no reason to believe that the narrator is unreliable. The brothers can even discuss their older brother, and it never need to come into consideration that they themselves are royalty at all. You can establish their backstory without needing to include plot points that you don't wish to reveal to the reader.
The downside of this is that the characters would not have the same emotional attachment to their quest until the reveal. This may work in your favor plot-wise or in developing your characters, but it might mean the journey is a little hollow to begin with as they would just be on a generic rescue mission.
It would also be stacking many reveals on top of each other (that the person captured is the heir, that it is their brother, and that they are also royalty). You can always space these reveals out, but the captive being who it is would need to come last, as the other things would need to come immediately after if they had not been revealed yet.
2. They don't acknowledge it's their brother
This is the "having your cake and eating it too" option. The brothers know who the captured person is, but they do not acknowledge their relationship to him. The reader never finds out what's really going on until you want them to, but the characters will act the same throughout the story as they know what's going on all along.
This can be done, and I've seen a good example of it. Following is a massive spoiler for The Banned And The Banished series by James Clemens:
From the very beginning of the 5 books in the series, the narrator of the entire story refers to the main character as "the Wit'ch" or "betrayer" etc. and it is immediately understood he holds incredible disdain for her. Over the course of the books in the prologues and epilogues he comes to understand the reasons why she made the choices she did, and slowly comes to forgive her. At the end of book 5 the reader learns the narrator is the MC's brother, and he acknowledges her as "sister", as he finally accepts the role he played in the story (which is significant), and realizes that it was he who was in the wrong the whole time.
The POV character(s) could simply refuse to acknowledge their relationship to their older brother. Perhaps he was abusive, or entitled due to being the heir, or they resent him for being next in line for the throne. They could simply refer to him as "the bastard" or "Prince Perfect", establishing their feelings towards him and never revealing that he is related to them.
The downside to this method is that you cannot go into much depth about their relationship with him. If you start to establish any sort of backstory between them, unless it's done very carefully it may become obvious that they are related. You might be able to drop hints about it, but if you want it to come entirely out of the blue it may be difficult to fool a perceptive reader for that long.
It also might make the reader question why they are rescuing him at all. If they hate him so much, why would they risk their lives and not let him rot, or not just send some hired goons to rescue him? They could maybe have been ordered to do it by their parents, or feel they have a duty, but it may be a little convoluted for the reader.
3. They don't acknowledge that they're royalty
It could be just a mission to save their older brother that they love, which later becomes a mission to save the realm when it is revealed to the reader who their target is. The readers get to find out who the characters are, why they are doing what they are doing, and what the relationship and backstory is like between the three of them.
This allows you to establish to the reader all of the backstory much better, and the reveal can come much later in the story, as it is realistic that they would journey to rescue their older brother without any sort of additional motive needed.
However, much like option 2 you would be limited in how much backstory you can give. You would have to focus more on the brothers playing in a garden as children as opposed to any memories of official functions. Perhaps you can let on that they are nobility, so they could reminisce about attending fancy banquets without revealing who they really are, and if they are well-mannered and trained in weaponry then it may be difficult to ignore their backstory altogether.
You would also need a convincing reason for them to not even think about who they really are. Perhaps they are ashamed of being royals and just want to be ordinary folk. But you would also have to avoid the reader questioning why their older brother was kidnapped in the first place if he is supposed to be just a nobody.
There will be more options, but those are the best 3 I can come up with. However, I would encourage you to read this about whether to put the plot twist in at all (which is more an answer to your other question, but it relates to this too).
Having a normal Hero's Journey, which has a huge plot twist in the middle and then resumes as normal, is entirely exploitative to the reader. If it's supposed to function as a big shock just to engage the reader without any thematic reason, then it might be better not to include the twist at all.
However, including the twist and having it as part of the theme of the story can be incorporated into any of the three options. Whether that's 1) trickling gradual reveals about the main characters into the story, 2) a story about rebuilding a relationship with an estranged sibling, or 3) having them come to accept their responsibility as royalty, the way the secret is kept from the reader, and how the eventual reveal is manufactured will be very important to the overall arc of your characters and your story.