Thank you for contacting us. I am happy to help you.
As I can understand you are using 2 widgets and defining each language per widget.
Since this feature is for classic widgets and I am not sure how correctly is this feature working, why not translate the widget into String Translation?
It is a simple text widget and you can have different content per language.
I use classic widgets. I didnt install string translation, why add more and more plugins, if there are features.
Oh I forgot, the features doesnt work. Why fix it, when you have additional code, which slows down the page and you need to go to other menus for translation (more complicated), instead of fixing bugs?
Oh I forgot, cant be fixed with a short reply and would be work...