I had to register to respond to your post... been there, done that! We are a few years ahead (youngest is 5 now) and life looks a lot different.
I have a similar story to yours (got married young, had kids in quick succession, super introvert, husband has stressful job) except I am the stay-at-home mom. When we had our first, it was overwhelming to me to realize that I would NEVER be alone again. Not only would I not be alone, I was stuck with an irrational, screaming baby. It sounds like your wife is struggling with PPD, and I believe you said she is stubborn, so she is unlikely to seek help. I too (also stubborn) struggled with PPD and refused to admit it. We struggled for several years because we had 3 instead of 2 kids, and third one was a terrible baby who made life even more difficult.
Now that he is 5, we are finally starting to enjoy life again. I get to be alone for significant periods of time! We are able to sleep through the night. We can even tell them to amuse themselves in the morning, so we can sleep in. I think the 0-4 stage is god awful for introverted parents. Focus on survival for now. If your wife won't go to counseling, you go. Talking to someone without a vested interest is so helpful (get someone who has kids and has been there!). Do whatever you can to help your wife with the transition. Figure out what is really bothering her. Is it the isolation? The sheer amount of work that two kids under 2 takes? Is it feeling distant from you? She may not even know what it is.
Once you know what is really bothering her, do ANYTHING you can to help her. If she needs a girls' night out, babysit. If she needs help cooking, bring dinner home (which was one of the best suggestions in this thread!). If she needs help during the day, get a babysitter two mornings a week. Don't just tell her how much you appreciate it, show her. It will mean a lot to her.
Kids put an enormous amount of pressure on a marriage in the early years (and I'm sure in the teenage years too - we are just not there yet). Survive the next two years before you make any decisions about the marriage. Once you get some emotional space when the kids are a little more independent, start working on your real issues in the marriage. My husband and I definitely still have issues, but at least now, I have a clear head to tackle them. Don't do anything rash while you have infants and toddlers. Your wife will probably mellow a bit as the kids get older. Right now, she lives in a constant fight-or-flight stage. Try to be the best husband/father you can until the little one is 2 or 3, then seriously tackle your longer-term issues with your wife and make a more rational decision about the marriage.
I don't know anyone (who actually remembers what it was like) who would say the best years of their marriage were when their children were babies and toddlers. You're not alone! Hang in there. It does get better.