Hulu Live

T-Mobile always assigns your publicly visible IP address (unless using a VPN). Hulu utilizes IP-based geo-location services for that address which really amount to nothing more than a wild guess.

A separate router assigns a private IP address which can be static (depending on how that router is configured). This will also result in a double NAT (network address translation).

Anything connected to that router will still be using the TMO public IP address.

P.S. Sorry to say this really isn't a TMO issue, but rather a content provider issue for those relying upon inaccurate IP based geolocation services. Content providers relying upon a device's GPS don't have this problem; however not all devices support GPS. FWIW, YouTube TV and others are a little more forgiving and don't require jumping through hoops to update your location as needed.