Millie -- please bear with me here. I am not posting this in order to kick you when you are down and I hope the following is not too harsh:
Me: What exactly are you unhappy with me about?
-- Don't bother asking him this any more. Beryl is absolutely right here. YOu are handing yourself to him on a plate.
DH: I want you when you are off work to do more, to clean the shower and Hoover upstairs, and do more than usual. You shouted up to me yesterday when I was putting DS to bed, he is my DH too it's not for you to tell me how to parent (I do think he is right with this, I probably was out of order)
-- See how he takes you up on your offer?
The answer to this is 'I am sorry you feel that way', followed by silence.
From this point on you were sunk.
Me: Do you not think given that on Monday i was potty training DH and still managed to make the beds, Hoover, cook dinner, unload the dishwasher and clean up dinner that first day it was enough?
-- Now he has you: you are engaging with him on his terms and he has won this round. Never engage with him on his terms, which you do here. This is you on your back foot treating him as if he has a right to demand and responding as if you have to justify and demonstrate that you are complying with the swishes of your lord and master or find some acceptable excuse to present to him.
DH: you could have cleaned he bathroom on Tuesday whilst DS was having a nap.
--- He again takes what you are giving.
His just playing with you now, waiting to see what you will put in his lap in your next response that he can use against you.
Me: I could have, but I sat down and had a cup of tea and read my potty training book, then you walked in from work. You didn't 'catch me' doing something naughty, I was sitting in my home having a cup of tea. I am allowed to do that, when I am on holiday from work.
-- And there it is: watch what he does to this in his next response.
A good effort on your part, but he still has you on the back foot, you are still engaging on his terms - justifying the fact that you sat down with a cup of tea, and you have not challenged the basic problem here, which is that he wants all the power in this relationship and will get it by enforcing the concept that you are his employee, that you answer to him, and that he has a right to make demands.
DH: (I know he will use this one example) well it's one rule for you and one rule for me, when you came home from work last month you had a go at me because the kitchen was a mess, but I can't have a go at you because you haven't cleaned the shower while you have been off?
- So he basically blows right past your reference to fairness and rationality and reason, and reveals that he is keeping score and playing the 'You are mean and unfair to me' card, just as his parenting comment was playing that card. In his heart of hearts he knows you are scrupulous about fairness and he sees that as a weakness to exploit against you. His radar is out for signs of 'weakness' on your part (and all other signs that you are a normal human being). He does not actually care about fairness at all, Millie (heck, in his heart of hearts he doesn't actually care how clean the house is, truth be told) hence the score keeping. He is one upping you here, not trying to make this fair. He is never going to be fair to you. All he wants to do is win every conversation you have.
Making you feel you have been mean or unfair to him results in you second guessing yourself whenever you want to challenge him for bad behaviour in the future.
As a result of his insatiable desire to 'win' (which will mean you losing every single time, for years and years and years, because he will never get enough of this ego trip) and his refusal to be fair, conversations about issues in your relationship are going to get nowhere. Worse than nowhere in fact -- you are going to be driven mental by this man because nothing that he is doing or saying is rational or reasonable. You know this, deep down, and your brain is desperately trying to find an ounce of rationality here by means of conversations with him where you hope against hope to be heard and understood and to make a change, but for your own sake I implore you to stop. It is like chasing your own tail. Your equilibrium is going to be the only casualty here.
You need to disengage. Try to start doing that verbally, by trying to detect power plays (i.e. comments about cleaning and how you spend your time) and countering them ('sorry you feel that way', 'what a shame you feel that way', etc). Ignore the BS (the details about cleaning, etc., which are really just a convenient handle he has decided to grab onto; he doesn't care about how clean the house is) that he flings at you, and confront the elephant in the room directly -- the elephant is the conceit he has that he rules supreme in this relationship.
I posted earlier that you should go to Relate, but I am now taking that back. You yourself need to do the Freedom Programme with Women's Aid and get your mojo back.
Do not go to couples' counselling with this man even if he begs.