If you are unable to find a way to run MCPE in the background (i.e. FirEmerald's suggestion doesn't work or isn't what you wanted), you might want to consider hosting a server with custom software. It may be a little advanced, but PocketMine-MP is great for hosting servers on desktop computers. Since PocketMine-MP hasn't officially update for the latest version of minecraft, you could use this version to get started. Once you install and run the setup, the server should be available to everyone on your local network. Since you are not running the game, you can minimize this window and run it in the background.
Here's more information on Genisys (the specific version of PocketMine-MP that I mentioned earlier)