As someone who crawls around the deserts of the southwest I can attest to the benefits of window tinting. If you go that route I'd recommend two things: check online about Maryland law regarding window tinting so that you don't get something darker than your state law allows, and ask around online or offline for recommendations for a place to do the work as some are definitely much better at tinting than others. About the hitch I can't say since I've never towed anything in my life.

You might post up to the Corolla forum and see what the members there say.