I feel your portrayal of Hal is realistic. Likely most men would feel similarly in his circumstances.
Granted, there are plenty of romantic novels of the bastard son happily serving his half brother and feeling grateful for the opportunity and acknowledgement. Or graciously declining with no hint of negative feelings while they "make their own name".
Or falling immediately in love and striving to change the opinion of their intended....etc. Hal's flaws make for many more possibilities in his growth in the story.