Firstly, you have learned from experience now - it is best practice to design the infastructure so that all environments (dev/test/prod) are as similar as possible, with the same versions of the OS/applications/IE/resolution/etc. Environments must be predictable which means persistant and consistent.
Resolution should only be an issue if you are using exact coordinates of an element to locate it's position and use it. This would be the case if you built a Surface Automation interface using Region Editor. If you are using one of the main technical adaptors to spy/identify your applications (Win32/Accessibility/JAB/etc) - and are not ticking attributes like x, y, width, height - than resolution will have no impact on the running of your interface.
If you are using Surface Automation and you cannot guarantee the resolution or position of screen elements, than Region Editor elements should not be used. Instead every element should be found and used based upon Image Recognition logic - finding the element position at runtime rather than relying on it to be in a set location.
If screen resolution cannot be guaranteed
