Printers are smart enough not to steal designs and sell them. They are in the business of printing shirts, not selling shirts. It's more lucrative for them to keep their clients rather than steal from them.
You really can't protect "ideas." Designs can be Copyrighted; Brand names and logos can be Trademarked.
Designs are technically copyrighted once they are in fixed form, but you would need to register it to have formal legal ownership. But keep in mind, only the exact design is copyrighted. Someone can take the same idea, design it differently, and that would be legal for them to do so. You can get more info from the
copyright office.
You can use the ™ symbol next to any brand name or logo you want to claim ownership to. But to have full benefit of ownership, and to use the ® symbol, you need to federally register your mark with the
trademark office. But this doesn't automatically prevent anyone from stealing your mark and using it. You would need to protect your mark by sending a cease & desist and/or suing anyone who infringes on your mark.
How can I protect my designs from being stolen by others 
