Yes I am grateful to @Bluebellforest1 too, as this thread has been a lifeline for me at what has undoubtedly been the worst part of our very tumultuous relationship and marriage!
@LoveYorkshire I think you asked my situation, the truth of it is I don't know! A few weeks ago I was preparing myself to split but now I'm resigned to 'one more try'. I'm exhausted tbh. We've been married about 10 years, and together years before that and problems have always been present in our communication. Quite honestly I don't know why we keep flogging a dead horse, but H is adamant he loves me and wants to be with me and the children forever.
I spoke with the counsellor yesterday at an individual video session, then she spoke to H alone, to get a picture of us as individuals. Next week we'll have a joint session and start to learn a new way of communicating. I told her my doubts, as H is very much leaning in to his diagnosis I am concerned he will not engage with any feelings. For him his Aspergers is a shield, and he can not or will not acknowledge emotion. Apparently he experiences a sensory overload when he tries to, so it's actually not that he doesn't feel anything, but rather feels too much and in panic will present a very blank 'meh' reaction - as he did when I broached separation.
She did reassure me by saying that anyone with or without a diagnosis can re-learn patterns, and people without asd have as much trouble as those with in recognising and understanding feelings. She said our marriage may have to adapt (I'm thinking, how much more can I adapt here?!!!!!) and we will both need new ways to connect, god knows how long this will drag on for but she said so far our responses bode well for future happiness. I feel faintly optimistic but also know we've been here many times before with previous counsellors. She swears this way is more sustainable, which is what H needs.
H meanwhile thinks all is solved. He deleted the OW (online woman!) and game group, end of problem - tick. We are seeing a counsellor - tick. He's acting more affection to me - tick. He's spending time with me, not gaming - tick. And then last night told me he's taken his console to his office and might play the game next week with one of his IRL friends who has an afternoon off work. But he'll leave it at work so the temptation isn't present at home. 
I know this just means he'll end up gaming for hours at work, not get his work done, then be late home because he's lost track of time or have to 'pop in' to his office at weekends to catch up. I've seen the cycle before and know it will happen again. It doesn't solve anything because I'll just be waiting for him to slip back. I don't trust him, and will always be suspicious of his addictive behaviours. If it's not the game there'll be something else.
Apparently the OW has been asking this IRL friend about where H has gone, and H told him to say it's family issues and he won't be online. I told him yet again I have no issue with the woman's friendship as long as he's giving me some time too. If he's chatting with OW til 3am, then the very least I expect is he stays awake to watch a film with me once a week or so. Or if he can't manage to give me even crumbs of attention, then he cannot be surprised if/when I go to seek out similar connections with other men who do give me respect, companionship and are interested in me as a human being and not just facilitator of a comfortable life and 24/7 nanny.
He then suggested it might be best if we stop talking about it and move on. Of course he would like that! He fails to see that by deleting this woman he's actually made her more of a big deal than if he was able to simply limit his playing. I wonder now how much of the 'temptation' was her and how much the game itself? I know the 'crush' would have burned out the way it does with all his male crushes too, I wasn't worried about an affair in the traditional sense. I assume that OW and all his group now think I'm some psycho jealous bitch who won't let H have friends, but for us it's not like I presume their lives are. When they're not playing, they are engaging in real lives (I expect, if they are NT and not addicted to the game. H has said they have families and often tells me X is at the cinema, Z is with his wife and so on. The only one regularly playing all evening til 2/3am is the woman). When H isn't playing with the group of lads, he's playing with OW til the early hours. The group of lad mates don't see that. When he's not on the game, he's watching YouTube videos of the game. They don't see that. When he's not doing anything game-related, he's sleeping, while I'm caring for our family. They don't see that, as he presents himself as such a family man. I don't know why it bothers me what his friends think, I don't see them socially, but it does make me wonder how he presents me given how I've heard the totally inaccurate way he presents himself and our lives.