We were in an extended stay for about six months while we were waiting for our house to be built and had the same issue with our Apple TV and our WiFi printer.
It lets you connect to either a standard Ethernet port like any router and it lets you connect to two WiFi networks and use one for the internet connection and the other to create an internal network.
You basically connect any device with a browser to the internal network to get through the captive portal and all of your other devices will then work that are connected to it.
I picked up one of those in China about four years ago. At the time I was finding hotels would offer free ethernet internet connections but either no Wi-Fi or expensive Wi-Fi. This was cheap, easy, and fits easily in a bag. Recommend.
I purchased an older version of this...
https://www.amazon.com/TP-Link-Wireless-Portable-Travel-Rout...
It lets you connect to either a standard Ethernet port like any router and it lets you connect to two WiFi networks and use one for the internet connection and the other to create an internal network.
You basically connect any device with a browser to the internal network to get through the captive portal and all of your other devices will then work that are connected to it.