I'd say the letter could be shorter, my opinion/edit on the FIL letter:
Dear FIL,
Part of my recovery program is to make a list of the people I have harmed and make direct amends when possible.
I write to you today to apologize for the emotional harm and embarrassment I caused you at several events we attended as a family. My behavior was unacceptable and there was no excuse for my not exerting self control in my drinking, for which my poor words and actions were the direct result.
You also lovingly opened your home to me and my interactions with K and your wife were not always carried out with the utmost respect that they deserved. I truly appreciated all of your generosity and the wisdom that you have extended to me over the years. I respect you as a great man who sacrificed his life to serve our country, along with the sacrifices you continue to make to provide the best for your family.
I know that no apology can erase the past, I can only let you know that moving forward I am committed to showing others love and respect at all times and I hope that one day you can forgive me.
Sincerely and with love, Me
me: 30 H:30 tgthr:7 m:4 no kids 5 counseling sessions initiated by H as a LR: Oct 2012 long distance marriage b/c of work since Nov 2012 official BD: July 2013 nothing filed 1/1/14 I dropped the rope