Hi OP I have only read the first few pages of this thread so I apologise if things have changed or moved on now but I just wanted to share my experience with you.
After my DS me and DH didn't have sex for about 14 months as I had absolutely no desire for it at all and there were so many other things to think about. After those 14 months I did cone to realise that having an asexual marriage is not "normal" so I used to make more of an effort with DH and although I did enjoy having sex I felt like I was more doing it because I felt like I should as opposed to me actually wanting to.
The whole 'touched out' concept is so very true. After 12 hours of being pawed and climbed on by my toddler with his relentless questioning I then used to cringe when DH put his hands on me, even if it was just to hug me. I used to move away from him and twist out of his grip and I'm sure it hurt his feelings but in my head I was screaming "For fuks sake can I not just have ten minutes where nobody is fuking touching me!"'When DS went to bed I just wanted to be left alone, I needed to feel like my body was my own and unfortunately that included stopping DH from touching it too.
I breast fed my DS until he was 2yrs and 10m (did your wife breast feed as that makes things even harder I think) and it's been 6 weeks now since I stopped and I'm hoping my libido will return.
I would say that in that last 18 months (after the initial 14 months of no sex post birth) we've probably had sex about 15 times. We probably average about once a month and even now it still doesn't feel completely natural to do it as I still don't have any sexual urges or desires to have sex.
I still fancy my husband, I find him incredibly attractive but the part of my brain that contains a sex drive has been switched off.
Prior to DS I had the higher sex drive of the two of us so our current set-up is very strange.
DH did discuss it with me a few times but because it upset me it was never talked about it frequently. I used to get upset because I had no idea where my sex drive had gone, I had no idea why I didn't want to have sex anymore and so it left me feeling so confused. I avoided the topic because I had no explanations to give. My DH thought there must have been a reason why I didn't want to have sex with him, but there really wasn't and I felt like he was looking for answers that I couldn't provide and it became very stressful.
When he used to hug me or try and kiss me I would just freeze because I was scared he wanted it to lead to sex.
Having children can do very strange things to sex drives and relationships and my guess is that your wife may be just as confused and upset by it all as you are.
I knew our marriage was suffering because we weren't having sex and I knew I was the reason for that which is a very heavy burden to bear. I really wish there had been a reason why I didn't want to have sex because at least then it could have been addressed or we could have tried to fix it, but like I said, it was nothing more than the fact my sex drive had completely gone.
I don't know what the solution is - I bet my husband didn't know either - but YANBU to want to have sex with your wife.