While the XAML files won't be the same, I suspect the namespaces will be different, so you could always fully qualify the other XAML name when you open it:
new SecondProject.Company.Class.MainWindow().Show();
A better bet would be to rename the actual physical class name for the second instance of MainWindow. To do this, you have to change the name of the class in the Code Behind file, and change the x:Class attribute in the XAML file to use this new name.