Running Don't Starve Together causes entire home network to destabilize until everyone is in the game

So we've been having this absolutely weird comedy of issues where our home LAN network just... goes haywire whenever any of the 3 of us have the game open and are not actively in a world. If we can all manage to connect to a game server, it quickly restabilizes. It has fewer issues if we're trying to browse LAN games, but even that does not work particularly well, and while the network can handle all three of us being in a voice call while in game for several hours, connecting to a voice call while the game is open but not in a game world just... doesn't work. At all. This only occurs with this game, we have had zero issues with other multiplayer games.