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I figured it out... it's An American Tail

http://www.childsplaypr.com/cpc-press/weesing/photos/DVD.%20Sillyville.JPG



Would this be it?

It's about a mouse and he wears a poorboy hat and a red shirt. I don't really remember many details about the movie, I just remember loving it and am really stuck on the name.

I think it may...