I gotta say I don’t really understand the OP’s question. It’s not like you and your brother play on two different boards. If he frequently makes plays that leave the board in a cluttered state, well, then you and he end up having exactly the same options as to what you can put where. If you’re just complaining that he doesn’t open up TWS’s for you willy nilly, well, that’s just sound play. If you’re saying that he constantly leaves the board in a congested state, and then wins, then clearly he’s better at playing on a congested board than you are, and plays to his strengths (whether consciously or not). Assuming I’m understanding what you mean by “congested board” properly, probably the best single thing you can do is learn your 2-letter words and as many of your 3-letter-stems as you can, because that will make it a lost easier to attach your words.
And being willing to trade in tiles is definitely good advice, although not necessarily directly related to board-cloggedness. If you have perfectly good letters but nowhere to play anything, trading in isn’t going to help you, most likely.