Basically OP he is in massive avoidance mode.
It may be because he feels totally out of his depth holding / interacting with the baby alone, so he would literally rather find anything else to do so as to create a smokescreen of "busyness"
He has no idea that you are at the end if your tether because he has never been with the baby to get anywhere near that point. Plus he doesn't want to hear it.
He would rather blame you as moaning / hysterical than shine a light on his own incompetence and failure to bond with his child.
Was he always doing all this car washing and gutter-clearing before the baby?
Most importantly however he is a TOTAL WANKER for calling you a "nasty bitch." How dare he!!! You gave birth to his child only three months ago. This is vile language to your worst enemy, let alone your wife! I don't believe it 
That insult alone requires immediate action. This is what I would do -
Pack a bag and go to your mum's tonight. Tell him you are devastated by what he called you. You can't respect or trust him at this time. You can't cope, he is not hearing you and you fear for your mental health. You have to put the baby first and you have to look after yourself as sole parent. As he won't look after you, or his own child, for even one hour, you are forced to go to your mum in desperation.
Tell him he needs to have a good think about his priorities because they are f**d. Tell him you see straight through him and all the window cleaning, etc is total bollocks. The only person he is fooling with that is himself. His wife is falling apart in front of his eyes and what does he do - fix a tile!!
Do take action OP because he needs a shock to the system.
Lots of men are like this. My DH was slightly, if I recall, but if he ever spoke to me in that language, it would be very hard for him to come back from it. Where is the respect?
Good luck! If you can't go to your mum's for any reason, tell him you are ringing social services or your GP / health visitor first thing tomorrow as they are your only option for some help and support.
I hope he sees the light very soon, but please don't let him get away with it.