Trades will go through and players will move in weekly leagues if the player's team has not locked yet.
You executed the trade before Brodeur had played a game this week (technically in a trade he'll lock at 3AM ET), so he moved. If you executed it today, he would not have.
Your best bets 1. Go to Commish Options>Edit Rosters and then Commish Options>Set Starting Lineups and insert Brodeur, and then next week move him back 2. You can go to Commish Options>Edit Past Box Score on Monday and add up his points and add them to DogRiver's team next week.