I travel a lot, and hotel networks are a total gamble — sometimes solid, sometimes barely good enough to load email. Mirroring over them works only if the room TV is on the same network and the connection isn’t overloaded. I usually rely on an app that doesn’t require logging into the TV and connects as long as both devices share a network. This one
Wirelessly mirror iPhone has been the most reliable for me. If the hotel Wi-Fi is slow or isolated per room, I just use my portable travel router to create my own little network and the mirroring stays smooth.