WiFi routers should pass any traffic transparently unless its configuration is really messed up.
If we ignore a configuration problem and you see any SSL errors, the only possible reason I can think of is that there is a “proxy” between your computer and Google servers, which decrypts and then re-encrypts your data for “inspection”. It basically means that the secure channel from Google is terminated on a server that your computer talks to without you realizing it.
The chances are that your router is partially set up as such a proxy so that it causes SSL errors. Corporations often use such proxy servers to monitor use of social media from office computers to prevent leakage of confidential information.