OK, so you've noted your responsibility in not quickly disclosing to your W as well as the reality that the woman who "outed" you may have had some motives which really are inconsequential.
Also, you are OK with not being poly yourself, yet continuing to be in an open M as you believe your W will likely wish to, at least right now.
So that said, we come back to rebuilding trust.
I think what you are doing is great, just realize that you can not PUSH someone to trust you. Even placing your phone where she might find it, is a bit of a push. She may... or may not... look at your phone.
Establishing trust is a fairly systematic process. If you say you are going somewhere, go there. If you say you will be somewhere at a certain time, be there AT that time. If you say you are going to get something at the store, go to the store and get what you said you were going to get. Consistently follow up your words with actions that prove the words.
With trust regarding being open and transparent, that will be led by your W. If she asks you a question, be open and honest. No lies, not even "white" lies. Be factual and provide no excuses or reasons. If you give excuses or reasons, she will possibly feel you are trying to "sell" her, so even if you are being truthful, she may THINK you are lying, due to the broken trust.
But don't tell her you are going out with buddies and then take date stamped pictures back to her to prove you did what you said. That's pushing and could possibly offend your W. She will want to make up her own mind, in her own time, and that's her prerogative.
The books were written in the order of DB and then DR. Now a lot of the content is the same, although they were written in a slightly different way. DR is almost like a "DB for dummies" book. ie. There's stuff you can follow directly, like a workbook. I don't think it's a matter of which to read first. Just read them, even if it's a chapter of each, each day or week. Many people just devour the books in a couple days, each.
Good on the 180, also think of some other 180s you might do which either you feel are good for you or your W may have made a valid complaint about.
Regarding the father's day thing. Is that "normal" for your dad not to invite your W? I really do think that you need to have a conversation with him, regarding if you misread the invite. ie. Ask him if he specifically did not put your W on the invite.
If it was an oversight on his part, and he would be OK with your W being there (as would others, if they won't be offended or awkward over her being there), then certainly ask your W. Just don't expect her to say, "yes".
Speaking of which, work on yourself, become an even more amazing guy that only a fool would leave. Keep your hopes down and your expectations near zero. And keep moving forward.
