The writer is using Ethos as in the first paragraph, she bonds with the congressman who she is writing to.
She is also obviously an expert on what she is talking about. She is constantly talking about all the figures the FBI or some scientists found during surveys and experiments. This is also using Ethos, making the congressman she is writing to respect her because she knows what she is talking about.
The writer can also be see using Pathos. Pathos is persuading the audience by using emotional appeal, values and beliefs. This is clearly shown when the writer writes about his sons death. It is also shown when throughout the entire letter, the writer obviously has very strong beliefs of what is good and bad.
Lastly, the writer uses Logos.
Logos is somewhat the same as the part of Ethos shown above, but it is basically being very clear and having evidence to back up your claims.
The writer does just that throughout the letter, giving clear reason why the congressman should limit the use of guns and giving lots of evidence to support here reasoning.
All in all, the writer did an excellent job of using Rhetoric.