It's not snooping or spying on her .... it's holding her accountable.
If she doesn't want to be held accountable for her promises and assurances to you - then you're just left presuming she's still having her affair and you have no reason to snoop or spy because you know what you know.
As far as this her moving pictures around and acting like she needs to detach from OM slowly ---- that's kind of like an alcoholic saying he/she needs to just finish out the liquor in the liquor cabinet or hang out in a few bars drinking soda because they miss the camaraderie of the bar before they actually quit drinking.
I feel some of this all comes down to proper "framing". You aren't "pursuing" her when you check up on her and hold her accountable. Instead you are ATTEMPTING to team up with her and solve/work on a JOINT issue. The joint issue is - both of you aren't in love with each other but we have children together and we took forever vows so "WE" need to see if "WE" can make this work before throwing in the towel. As you told her AND the kids the other day ---- "it looks like we are divorcing". I'm not your keeper. The cage door is wide open. Go be with OM and continue making the biggest mistake of your life OR end it with OM once and for all (which you fully understand is a difficult thing to do), and commit to working with you (TOGETHER) to rebuild/build a marriage of extraordinary care.
The reframe the boundaries as a joint boundary around your seedling of a marriage recovery. No contact with OM is the foundation but you can frame that too as the three foundational pillars of initial recovery - honesty/truth/accountability.*
****edit to add - Stumbling through "no contact" is common. It's a mistake for her to have closure contact at all but they sometimes just can't help themselves - it's more important that she shares her stumbles with you - in a timely manner - before you even look for it or find it. You TRY to indicate that when the urge comes upon her to call you instead or some other way to avoid the trigger response but no matter what you won't hate her if she simply tells you immediately and works with you to tie up the "no contact" loose ends even better. Remember too - OM could break "no contact" himself - so she needs to strategize WITH YOU HER ACCOUNTABILITY PARTNER how to handle that appropriately as well.
There is an opportunity here to lead by example. There are websites that you can register with that will monitor your web/internet activity and send your wife an email if you search or visit XXX porn website and material. You could sign up at one of those website to let her hold you accountable. Maybe instead you just put a key logger on your devices and have her set up a passcode you don't know. The power of accountability is NOT that your wife is going to be watching you 24/7. The power is people behave better when they know the are being (or could be) watched and/or their behavior is being recorded.
Accountability is one of the most beneficial (for self and society) roles of marriage. As society bifurcates more and more, there remains less persons for us, as individuals to be accountable to. It used to be you were accountable to your spouse, parents, grandparents and entire extended family as well as your neighbors, church, village and clan. Now people are so disconnected they can do pretty much whatever they want and no one in their extended network ever has to know or find out about it unless they just happen to stumble upon it. I heard some pretty weird and very private stories from families cleaning out the homes after a tragic sudden death of their single 20'-30' something children. It's probably one of the biggest reasons married people outlive single people - someone is holding you accountable for your behavior to some degree.
The internet is 90% complaining and entitlement and I hate it because I deserve better!