I hear you completely. We have DD1 2.5 years and DD2 7 months. First was a nightmare sleeper and that took its toll. Then various other complications made the first 4 months of DD2 very stressful.
I saw a group of my friends when DD2 was about 5 months old and was in floods of tears because DH and I just weren't getting on at all. We just bickered and shouted at each other. it was awful. I really really just wanted him to move the hell out so it would stop.
Every single one of my friends said they went through something similar with a newborn and toddler. They said just ride it out and try to be more forgiving of each other. I'm only a few months on and I think they were right.
I'm getting more sleep which is helpful, and DD2 is getting ever so slightly easier.
On the surface if looks like an easy-ish baby and OK toddler shouldn't be too hard. But bloody hell, every single pocket of time is eaten up and neither of you get a real break. Popping out for an hour is suddenly a bigger deal too because one of you is leaving the other holding two littlies, which isn't anything like leaving one parent with a 2 year old.
I say, it's normal to snipe at each other during pressurised time. Don't worry that you won't make it, you will. But do talk to each other about how hard it is and how normal it is.
We've only just stopped talking about divorce in the last 2 weeks, and I'm now starting to realise how crazy we were to even mention it. The stress has to go somewhere, and I think the parental relationship takes the brunt.