I remember struggling with this (specifically whether my situation was "different enough" from others' to warrant a letter to H in which I acknowledged my responsibility in the breakdown of our M). Such a letter would certainly classify as "pursuit" to me. But I told myself that it was prudent and good-judgment to apologize for my role.
... until I took a long, hard look at the facts.
And I reached the conclusion - with some help from friends here - that an apology to a spouse who is actively cheating (even if we have things we would do differently now) is just plain backwards. And pointless.
I get the sense your mind is already made. But I'd be sure to ask myself what my goal is in sending the letter ... and whether I'm *genuinely* doing it for a benefit to myself ... or if I'm hoping for a result. If you're hoping for a result, then I think you have expectations attached. And to be honest, I'm not sure that any of us who are hurting so badly from betrayal could actually pen a letter and send it to our wayward spouses with no expectations and with the TRUE goal being to help US. It just won't.
And if we could jump into the minds of our wayward spouses for just a moment, we would see why such a letter wouldn't have the desired impact on them, either. Since my H has been back, I have been *floored* to read some of his thoughts at certain times through our separation. I had totally felt, from his interactions with me then, that he was being friendly and even showing signs of having doubts about his decision to be with OW. But the things he was telling others at that time?? Wowzers. All I can say is I am SO thankful I never apologized to him while he was wayward.
M: 40 H: 44 Married 14 years S11 & D6; D20 & D19 from previous M 2BDs/PAs, 8 years apart Piecing: April 2014