Thanks Vasu, the web part has the "Translate field" checked but refuses to translate the custom widget.
And yes, I did go over the Language documentation few times.
"Translate web part properties" is checked under "Translation Properties".
Also, "Automatically import translated submissions" is also checked.
Google Translation API works just fine because the page gets translated with the default Kentico widgets except for the custom widgets.
I tried hundreds of times, deleted the page versions, clear the cache, restarted the server... with no luck.