This could only mean "Your brothers read/study every day" because तेरे, पढ़ते, and हैं all indicate a plural subject. "Your brother reads/studies every day" would be "तेरा भाई हर दिन पढ़ता है."
I was about the check/make the same point as BobEaton4 above... If you were speaking respectfully of someone's brother, perhaps the plural form is also possible...? IDK...
They do say: मेरे पिता भारत में रहते हैं । but I haven't yet seen an example using तेरे being respectful plural/sing, if you know what I mean...!
Ah, I see what you're saying... Yeah, I guess it would be possible in that situation. Though I would think if you were speaking respectfully of the brother, you would also show respect to the person to whom you're speaking and use आपके instead of तेरे.
A parent might use the original expression to their child with an older brother to help them learn respect forms. But you are also correct, I've heard parents use आप to their children for the same reason