It's a perfectly valid sentence, and the repetitiveness may just be a matter of style. You could also say
Ich hatte das Gefühl, dass ich mich auf Euch verlassen konnte, so wie früher auf meinen Bruder
without changing the meaning.
In other cases, contracting a sentence like that can lead to ambiguities, like in the famous joke:
"Ich träume davon, Millionär zu werden, so wie mein Vater"
"Dein Vater ist Millionär?"
"Nein, aber er träumt davon"
The ambiguity could be resolved by saying
"Ich träume davon, Millionär zu werden, so wie mein Vater davon träumt"
But not in your case, there is no such ambiguity.
By the way: In English, it's similar. The grammar here may be a bit odd, and I think you wouldn't say it exactly like that, but it's just intended as a comparison:
I had the feeling that I could rely on you, like on my brother
I had the feeling that I could rely on you, like I could rely on my brother