That's such a hard situation, elbow27. Complex indeed. Is your therapy tackling the addiction itself or the underlying issues? If it's focused on the symptoms rather than the cause, that might be a reason for it not helping as much as it should. You could ask your therapist to refocus, or perhaps look for other approaches to the problems.
The reason I ask is because I can't see how adding context will change the situation with R right now. She might understand you a little better. But it won't help her trust you or open any doors to a future connection. And it risks coming across to her as trying to "justify" it, which is clearly not what you intend. Whereas taking steps to make permanent changes, might demonstrate how much you regret what happened and how determined you are that it won't happen again. And that also gives you something positive to focus on for now. I think she'll need some time to get over what has happened, not just your betrayal but the public outing of it all.
“We think too much and feel too little.
More than machinery, we need humanity.
More than cleverness, we need kindness and gentleness.”
Charlie Chaplain in The Great Dictator