I know you've gotten tons of advice but I wanted to chime in. See I'm in the unique position of having been in both yours and your brother's position.
When I was 15 both my parents remarried, both new spouses had young children. The youngest was 13 years younger than I was, the oldest was 6 years younger than I was. So by the time my youngest sister was 16 I had a 3 year old son also.
The first thing you need to do is get it out of your head that your "angel" wouldn't or couldn't POSSIBLY start fights with a 17 year old simply because he's 3. Because he CAN AND WILL. And he'll do it precisely because he's 3.
The second thing you need to do is teach YOUR son boundries of what is and is NOT acceptable behaviour towards those older than he is. Your 17 year old brother may not technically be an adult yet, but he's close enough and should be treated with more respect. Also teach your son that Uncle's room is OFF LIMITS unless Uncle specifically says it's ok. And that includes NOT standing outside the door and knocking constantly (or asking can I come in, or whatever) until he gets his way and is let in just to stop the annoying behaviour.
The third thing you need to do is sit down calmly and quietly with your parents and your brother and find a way to compromise on the whole issue. Let your brother know that you respect his needs and his space as much as (if not more) than that of a 3 year old.
You have no idea how frustrating it is for an older child who has no recourse against a tyrant of a younger child. Especially if that child's parents refuse to believe their little angel could be doing ANY of the things the older one is saying they are doing. I've lived that and it's NOT fun.
When my son was 3 and my daughter was 1, we went to stay at my mom's for a month. And the very first rule I laid down for my kids was that Aunt Ninny's room was completely OFF LIMITS unless she specifically told them they could come in. They weren't to pester her about being let in either. And there were swift consequences if they broke those rules. And those consequences happened EVERY TIME they broke the rule. It didn't take them long to learn and respect that that room was Aunt Ninny's private space and was to be left alone. And in return my 16 year old sister was MUCH more willing to help out with the kids and hang out with them when she was ready to. She's also turned out to be their favorite aunt.
But to solve all this you're going to have to have a conversation with your parents and your brother. And be WILLING to HEAR what your brother and parents tell you about your 3 year old and his behaviour. Take steps to correct what needs corrected and come up with a compromise for everyone.
If that doesn't work you may have to find some other child care.
Good luck and I hope I helped some.