Oh boy!! This is a challenging situation for sure...no two ways about it.
Speculating about a person's sexuality is just that...speculation. The main issue is that your W is now with OW. Not too different from 325 DBers here. If your W was with an OM, would that make things different and alter your DBing? Nope...DBing is the same principle across the board here.
Now to the real nitty gritty here. I think there are some valuable takeaways here, HWA.
1) Your sons' seem not to feel comfortable with you nor trust you for whatever reasons of their own. I think it goes back to the tattoo controversy and it just snowballed from there and on. To bury it for once and for all, don't do anything like this again. I was afraid that it would have been a serious setback for you. I do hope you recognize and realize the seriousness of this matter.
My suggestion is to work on your relationship with your sons. Meaning taking a more open and interested approach to them. Ask them open ended questions about their interests, hobbies, dreams and aspirations. Perhaps offer to help with house/car/truck projects as means to bond with them once again. This means NADA, NEYT, NON on W and her situation. Sure, if sons bring up past memories of their Mom, you can say a something positive about the memory.
2) STFU about your W to friends and family...drop questions and fishing for details about W. These questions make them uncomfortable because you put them in the middle and they feel put on the spot. No one likes that at all.
For now, the main focus is to re-build your relationship with your sons. Call them up for chats, perhaps dinner once every two weeks, then have them cover for cook outs. You get the picture, HWA.
Are you able to do this?
And what is the date of your first encounter with W and the OW?