Perhaps. While an agent may refuse to short-check the bag in HYD if they see you are going all the way to Denver and you might be charged UA baggage fees if you tried to re-check one of your bags at IAD (while pulling out the other for your brother).

I would advise you first tell the Qatar folks to only check you into DC. Then you would go to the Main Terminal rather than Midfield immigration terminal upon landing, collect your bags, and meet your brother, then walk to United check-in, get your IAD-DEN boarding pass, and finally proceed back through security to your gate.

If you are checked through to Denver, your bags will come off the conveyer belt at the midfield immigration hall at IAD and you will be re-united with your bag there, but if you try to take the drop-off bag through security as a carry-on, the darling TSA will likely not let it by. Plus, you'd have to take the train back to the Main Terminal, exit, then go through security again after dropping off the bag.

So a solution is possible, but it may turn out a bit messy. Do your best to get Qatar only to check the bags to IAD.