IMHO, I think you need to take things one day at a time and don't push for passwords and other information right now. Quit asking him about ow, and do your best to get her out of your mind (STOP thinking...picture the big red stop sign).
It's going to take time to rebuild trust in your marriage. I think the best thing for you to do right now is focus on the positives, celebrate the baby steps and enjoy the time your husband is spending with you and your daughter. This is what I'm trying to do, and it has worked WONDERFULLY until I slipped recently and had a little fit about former ow. All that did was set us back. We are back on track now, but it was nothing but a waste of time and effort.
Your husband probably feels like he's walking on eggshells with you and that he is going to be interrogated about ow every day. Show him that you are giving him a real chance to prove that he is committed to you! In your last post, you stated the good things he is doing - calling you during the day, being more affectionate and spending time with you. Thank him for those things!
As for your rings, they are YOURS, and you can put them on anytime you want. He can put his on anytime he wants. A ring is a symbol of your bond and love, but that's all it is...a symbol to the outside world. The two of you should know that with or without rings, you are committed to each other. Rings do not make a marriage.
Until you are ready to forgive your husband 100% for his past mistakes and quit hanging it over his head, you are never going to be able to move forward. Trust me, this is something I have to remind myself of everyday!
You can do this! Picking up the pieces is TOUGH STUFF, but you can restore your marriage!