And what should we do in order to make sure that the players are 100% connected?
I don't think 100% connectivity is achievable. The Internet is a huge mess of different protocols, restrictions and configurations. It's just infeasible to support every possible combination of networking and software setups.
The stock Multiplayer feature can achieve about 95% connectivity, which is pretty good. To beat that you'd probably have to set up and configure your own TURN server, and unless you are an experienced network engineer, you will probably not be able to beat 95%.
You could use some entirely different technology for multiplayer, like WebSockets to a central server, but Construct does not have its own support for that, so you'll need either third-party addons or a custom solution. That still may not achieve 100% connectivity.
I don't think the web provides any way to directly message over a LAN - you either use WebRTC for peer-to-peer connections (which the Multiplayer feature already uses), or you go via a web server.