You are creating different object of CommonViewModel in each user control, you have to create one object and assign them in both user control.
Create object of CommonViewModel in MainWindow
<window.resources>
<local:commonviewmodel x:key="ABC" />
</window.resources>
and then set data context for both user control UC1 and UC2 in your Main Window.
<local:usercontrol1 datacontext="{Binding Source={StaticResource ABC}}" />
<local:usercontrol2 datacontext="{Binding Source={StaticResource ABC}}" />
Thanks
Shrey Chouhan