When Ever we run the upstairs shower or washing machine dirty wate backs up the drain into my downstairs shower. I am assuming I have a clog in the main but do not know how to fx it. I tried using a chemical in the downstairs shower and snaking it but neither helped the problem.
Any ideas?

Stop with the chemicals since it will make the crrect fix difficult. You have a clog downstream of the lower shower drain, It happens to be the drain lowest to the floor so it backs up to that point and not higher. Is there a basement or crawl space? Sorry to start with a question but I need to help you find your clean out.