What thebody said. We only know the OP's side and it is ridiculous to suggest that she leaves and breaks up the family without knowing the full picture.
princessglitter - imagine you are your DH. Okay, now really imagine you're him - place yourself in his head for a while and then ask yourself what things you would post on Dadsnet about your wife.
No doubt both of you have small, medium-sized and even large irritations with each other. Stonewalling is classic male behaviour (NB: not all men, but it's fairly typical of most) when they feel unable to deal with an emotional problem. It is bloody irritating, bloody childish and does nothing to solve the problem. But it is classic behaviour. It wouldn't surprise me if the petulant half-arsed attempt at tidying was also a classic male thing, a sort of silent protest. And then, to be fair to men, I have to ask myself what are the classic female behaviours which annoy the hell out of men!
In fact, you might find it informative to do a web search on male/ female differences and see whether you come up with a list of behaviours which reflect your own experience. Hopefully you'll find something useful so that you can see that (1) you ARE normal, and (2) you CAN work through this stuff, as long as both of you work at it.
This is a really, really stressful time for couples, when your kids are young (we have two kids with similar ages so I sympathise since you have three!).
IMO you can't connect on a 'let's sort this out' level until you connect on a less threatening/ overwhelming level. So you both need to have fun together, as some people have already suggested. I do appreciate (from my own present experience) the challenge of having children that wake regularly. It is exhausting, let alone the fact that it makes it so hard to get out of the house.
Do you have a garden? Could you buy a nice bottle of wine and a pudding, and then sit in the garden with the baby monitor next to you, and play a board game/ do something else that doesn't involve an intense talking session? You need to say to your DH 'I feel like we're not connecting any more. You mean so much to me and I really want to do something about this. Can we try and do a fun thing together once a fortnight and see if that helps?"
I know all this is easier said than done, but take comfort that your problems are not unique and, if you fundamentally have a good relationship, your problems are solvable.