What happens when you open SketchUp? The terms of the subscription are that SketchUp can be used offline for up to 28 days (one month) before needing to re-connect with the license server. But there are some tricks and inconstancies in getting that to work.
Connecting to any other network, including your phone as a hotspot, should get you through in order to sign in. For features that need you to be online you would need to fix the router issues, to use that network.
This article talks about the ports that SketchUp uses, and how you could perhaps whitelist sketchup.com addresses to solve the router problems: