Copyright Law
A copyright refers to the owner of a particular expression of an idea, but not the underlying idea or method of operation. <--Direct from my business law textbook by Beatty/Samuelson.
Trademark
A trademark is any combination of words and symbols that a business uses to identify its products or services and distinguish them from others. Similar to Nike's "Just Do It" and Microsoft's flyin window logo, the Poss family uses "The Alabama Rig" to distinguish themselves from other companies, hence why we see names such as "umbrella rig", "school-e rig", etc.
Here is where a court would rule against the Tammy Poss and her threatening comments to kids on YouTube:
"Contrary to popular belief, a trademark does not give its holder a monopoly on the word, phrase, shape or color as such. Trademark rights are typically granted on the basis of a registration. Part of the registration is an indication of the goods and services that the trademark should protect. Only commercial use of the trademark for those classes of goods and services can be restricted by the trademark holder. Non-commercial use cannot be prevented, except if that use harms the distinctiveness of the trademark."
As you can see, people are free to use the trademarked phrase as long as they are identifying a particular product or service when it comes to discussion and informational reporting. What kids don't understand is that they cannot make their own umbrella rig and sell them under a trademarked name or use a copyrighted "version".
By taking this battle into her own hands, I think Tammy is creating a lot of animosity towards The Alabama Rig and it is a losing battle. While I can understand that the fishing industry is a copy-cat industry by nature, unruly customer relationship management and poor communication skills will destroy a company in a blink of an eye. Seeing as I got this entire situation from a "Google Alert", I would say the process has begun.