Welcome to SI. I'm sorry you find yourself here, but glad you found us.
I find my self lying about really mundane things that don't really matter like in day to day life
How can I reassure her that I will honor her while I am away?
These two statements don't go together. To answer your question, you can't. If you are lying about day to day little things, how CAN she trust you?
Why are you still lying?
The only way for her to begin to believe anything you say is to start telling the truth, consistently, over a long period of time.
This trip is extremely difficult for her and she has zero reason to trust you right now. Is there any way you can not go on this one? Is OW going to be on the trip? Put yourself in your wife's shoes. Would YOU trust you?
What have you done to change your A behaviors?