NameChange what did attract you to your DW then?
From what you are saying, it's not just the sex issue is it? Or is the sex problem then let to resentment etc...?
I personally can understand why she said it would be 'weird'. If you haven't had sex for so long and it was never great to start with, then I can see why it would feel 'strange' to have sex again (as surprising, out of the ordinary, perhaps even uncomfortable).
FWIW, I have been at her place. And I have been finding it easier to push the issue out of my mind rather than tell my partner I didn't like having sex with him (or that it wasn't fulfilling for me). I learned to live with no sex, got use to it and accepted it (as you would if you were single with no casuals). That's not the end of the world tbh.
I also notice you are talking about having sex, not making love (I know some people will cringe at that word) but for me having sex (ie meeting a physical need for sex) isn't the same than making love (ie a loving act). I would have been happier with making love than having sex iyswim ( but my partner would have been happy with just sex...).
There were a lot of other things that lead us to that situation, incl dcs (ie extreme exhaustion), sex life wasn't fantastic to start with, lack of support on his side (see exhaustion), lack of empathy/seeing things from my pov etc... Even kissing was an difficult thing for me because a kiss that would be more than a peck on the lips would be interpreted immediately as an 'OK to have sex' (same with a 'loving' cuddle etc..) so it was safer to keep away from that too.
Having said all that, I think that the idea of counselling is a really good one tbh. I don't know if it will help with restore your relationship, but it will give you some insights as to what it is like for the other and will allow you to decide what is the best course of actions.
FWIW, I don't think the dcs are a good enough reason not to get divorced. I also don't think that sex is indispensable in a relationship. Love is as well feeling loved but that can be done in a lot of other ways than sex.