I think neither Arslan nor Hilmes are the real sons of their fathers. It seems both brothers (Osloes and Andragoras) tried to avoid the prophecy by sustituting their own child with a stranger one or something like that. I don't know but maybe there is something in the ancient legend before the fall of the Snake king, it seems there was another legendary king (before the hero who create the actual royalty) and maybe Arslan will be his descendant or something like that...
Warning BIG SPOILER :
Arslan is not the son of Andragoras and neither Tahamine. When Tahamine asks for the child that was stolen from her she means that the baby she gave birth to was a daughter but Andragoras wanted a son to succeed him. So he gave the child of Tahamine for adoption and bought a son from a knightly family who is Aslan and made him crown prince. So they are totally not related by blood and he probably hates him because Tahamine hates Andragoras for abandoning her own child.
Hilmes is also not Osroes son but... Andragoras and Osroes' brother instead ^^"'. Osroes and his wife couldn't get a baby so the king at that time (Osroes' father) implemented a tradition saying that if a couple can't get a baby the father of the husband has to sleep with his daughter in law to bring good omen (ewwwww - -"). And this is how Hilmes was born... And in truth even Osroes hated Hilmes and asked Andragoras to make sure he would never become king of Pars...
Here is the truth, totally sad for both princes who asked for nothing but got all of this. Enjoy the spoilers... ^. ^
BIG SPOIL AGAIN :
It will be uncovered when Arslan marches on Ecbatana and meets his father during the battle. His father tells him the truth if i remember correctly (or maybe it's Tahamine who does i'm not totally sure). But Andragoras is killed by Innocentis (Lusitanian king) and Arslan becomes king. He decides to reveal the truth to people of Pars who decides to accept him despite that (because he freed them) and he also promises Tahamine to look for her lost daughter. He makes a call for information but many impostors show up so actually the daughter is still not found (i know it's crazy but i made my own theory that Estelle is Tahamine and Andragoras' daughter, it would be so nice!!)
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If he wasn't just so full of hatred, I would feel really sorry for Hilmes because you said even his "father" Osloes hated him and wanted to see him dead (the reason why Andragoras try to kill him). However, Hilmes loved his "father" and wasn't responsible for his "grandfather's" superstition. That's a awfull karma.
I must admit he is a terrible character but I cannot totally hate him. If he could find hapiness, I would be glad but I read some shorts spoilers and I know this won't happen. But, I really hate Andragoras and cannot feel a single drop of sympathy for him...
this is just really really good i didn't think i'd be able to finish this in 2 days haha
anyway, just some thought
maybe arslan is not the son of the current king/shah? maybe he is the son of brothers king and hilde is actually the king'son? kind of like exchanging the first born so as to avoid the prophecy? that's why he wants to get rid of him and that is why the queen does not like arslan? just thinking (〜 ̄△ ̄)〜