Expecting a hotel to have a router in the room is an interesting request. Have you ever been to Thailand? I've worked on hotspot (normally gives +50mbps) and regular internet. Just find a hotel that has signal. If you are doing intensive work maybe you need a router but I don't think it is entirely necessary.
Digital work is a gray area in immigration law across the world. If Warren Buffet trades a stock in England is it considered work? Well it is stock!!? Well there's this thing called Day Trading. The intent of immigration laws related to working is to take away the likelihood of a foreign individual stealing a job from a local. In this case there is no job theft.