Yes, it's weird, don't do it. He is already aware of your connection to his brother and quoted you a price -- it's not like you're a secret connection. Either that already IS his discounted rate, or he doesn't have a discounted rate, or he does have a discounted rate but you do not qualify.
Don't get me wrong, it's not illegal or anything to ask for a discount for whatever reason you think should get you one -- but in this case it would be tone deaf and inappropriate. He told you what he charges, you can either decide you want to pay it or you don't.