The legal answer to your question is that by coming up with the logo yourselves, and using it to sell T-shirts, you have already established trademark rights. The letter you mailed to yourselves didn't do anything (that's an urban legend).
However, if you are asking for business advice on how to monetize your new logo, I don't think we lawyers are the best people to advise you on that.
If your sons are serious about turning this into a business, they should form a 501(c)(3) tax-exempt corporation so they won't have to pay tax on the t-shirts and other tjings they buy.
As for a "poor man's trademark," your self-addressed mail confers no TM or any other kind of rights, but it might document when your sons started using the TM in interstate commerce - or it might just document when they started selling t-shirts in IN, which wouldn't acquire any federal rights.
Since you want to teach your sons about charity, you might also want them to learn about IP law and how to monetize ideas. Please see the "how to" guides with basic background information about IP and business linked below.
Avvo doesn't pay us for these responses, and I'm not your lawyer just because I answer this question or respond to any follow-up comments. If you want to hire me, please contact me. Otherwise, please don't expect a further response. We need an actual written agreement to form an attorney-client relationship. I'm only licensed in CA and you shouldn't rely on this answer, since each state has different laws, each situation is fact specific, and it's impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue.
Without a trademark registration, any trademark rights obtained in this new logo will be confined to the geographic community in which the use of the mark is made. For this reason, if they seriously want to protect their rights in the mark, a federal trademark registration may be worth looking into. For the basics on registration, you can go to the www.uspto.gov web site, but many people find the process to be safer and easier with a lawyer on the team to navigate. Good luck.