This is my first post, I have been a reader of many posts in here but never commented ...guess this one I should. I am sorry to hear what you are going through and I think perhaps I can offer a man's perspective on this issue as someone who may have gone through something similar in our marriage.
We have two DC, first, one came and was very exciting times but also crazy ..no sleep, business was crazy with me been self-employed and working a night job as I tried to set up our business during the day.
I had a very tough time but my Mrs has a worse time, I was Grumpy and short-fused most time when I came home, we both did want to spend time with each, so when our first DC was just over one year and my wife gave an what I took to be an ultimatum to have a second child or she would leave, this changed things big time....
I resented her and even hated her for what I perceived to be her not caring about what I wanted. I loved my second child but kept resentful of my wife. I really wanted things to work as a family and thought maybe the sex would bring us closer, I mean I still longed to be loved and to love her but no matter what we did we kept hitting a brick wall.
Now, we are well and our marriage is miles away from where it was.. I am happily married and love my wife and DCs to bit, so what changed: Two things;
First, I discovered that I actually was under depression the whole time after my son was born, so took some medications but really this did not help what helped most was therapy and counselling with my wife, where we laid our cards on the table and express our deepest feeling including the resentment I felt for been push for second child, once she explained her side of the story and said sorry, It was really easy to move from that.I also discovered that unbeknown to me I suffered PTSD from an accident in my childhood which sent me to a fight or flight mode everytime my children or wife would cry...( and my first Dc was a real crybaby). So please get him to go to the Doctors and also get some marriage counselling
Second, priorities on helping each other take some time to have break, i.e. for us we discovered helping each other have more rest and family time where you don't have to do anything stressful e.g. for us taking turns to let each other have a nap on the weekends then spending a lazy movies night together after early dinner helps us recharge the batteries.
I wish you all the best and just to be clear is not right for either of you to be in such as relationship but don't throw in the towel yet, try work things out and get someone else involved so that you can monitor the progress as this is going to be a long process, it has taken us about two years now to get to get to where we are but it has been well worth it ;