All the buttons have Command binding which can only be resolved if their DataContext is resolved. In this sample, each button's DataContext is set to an Editor which is part of Resources. Each of these editors has their Map property bound to a map, using Element binding.
Since you are moving this to a different UserControl that does not contain your map, Element binding will not work. You need to resort to other means of binding. Maybe create your own DependencyProperty (Map) in the UserControl so that you can use this instead.