I'm sorry for your frustration.   To make this easier to read, please break up the text with paragraphs.  Please also see the FAQ for abbreviations.  H or DH is used here on this site for husband, so your using it for the ex wife is confusing for example.

This man doesn't care about you.  Disengage from his children (you can read about that on this site) and make an exit plan to leave this relationship.  You are simply a convenience and this man is not worth it.

As a taxi service as free childcare more than likely a maid and cook even though you don't express this in your post. It is up to HIM to deal with the ex and pick up his spawn. That's HIS responsibility if HE can't do it HE will have to say no to his ex wife stand your ground maybe it will get better maybe it will get so bad you will have to leave either way is better than this. I would personally just leave his ass but I understand not everyone is willing or able. 
I would say have a proper talk with him to say you will help out sometimes but 99% of the time it's on him to be doing everything for his children if he starts putting you down just know it isn't about you. 
You are not the problem in this you are going above and beyond for him, his kids and his ex wife letting her live in your home etc. Take a step back and please realise you are an absolute diamond he is incredibly lucky to have found such a caring wonderful person who will do so much for him.you are allowed to say no to something you don't want to do. You are allowed to look after yourself and if that means disengaging from skids then that's what it means. 
My heart goes out to you. You definitely shouldn't have to deal with this 

Hi, sorry, I didn't read beyond you marrying him 6 months after you met while pregnant with another man's baby. That was enough for me to know the answer - get out, you made a mistake. And please stay single for a while until you figure out why this marriage seemed like a good idea. 

Well I would say the consequences of your choice to rashly marry a man you only knew 6months virtually have taught you more than I could ever reiterate to you. And I am guessing the examples are only the highlights so with that being said....Why do you stay? Is it because you are scared?  What are you afraid of? Is it him? or Is it your future without him? At this point I think we can all agree that what yall are doing right now isnt working or healthy for anyone and it is absolutely ok to stop doing things that don't work for us to find a new way that does. Marriage doesn't have to be a lifetime for women who are being abused anymore. Are you just looking for directions? Advice? or Just here to vent your frustrations? Because after being on this board for over 7 years I can already tell you the older posters will tell you to leave, they won't bother breaking it down for you. You just need to get out. There is better than this, anything is better than this and he will actually only get worse the longer you stay because you reaffirm his behavior by staying and taking it. 

You need to wait for him to go to work, move out taking your personal documents/belongings and then go to an attorney (consultations are lower/free and some offer payment plans) and file for a divorce. You do not need to be there when he gets home. Ask for help to make sure you will be out in time. Once you retain your lawyer then you need ot block him from your life. Anything he has to say he can say it to the person you legally hired to be your buffer. If your friend was in your situation, you would tell her to leave that asshole so take your child and go. If you have no where to go look out for local women's shelters in your area or in the outskirts of your area that will take you until you can make better arrangements. 

You've described verbal and emotional abuse from this man, and I'm guessing from the context of the situation, there's financial abuse as well. You don't need to be this man's servant! And you'd daughter shouldn't grow up thinking that the way he treats you is normal or okay to expect from a partner.

check your area and find the women's shelter to help you get on your feet but do not stay!

Get your bowling bag and get the h#$$ out of there.  Run like your butt is on fire.  That is what you do.  This guy is using you as a taxi service, maid, cook, etc.  His ex is using you as a taxi service too from the way it sounds.  Then they both get mad when you say no.  The word no is your friend.  Your husband is not.  

Make a plan.

If you have posessions you cannot leave behind. (just about anything can be replaced btw).. then think about finding a storage unit and slowly get your important things out of the house.  You may well have to leave behind a lot of stuff... furniture.. even your child's toys etc.. but again, that can all be replaced.

Seek out a women's shelter in your area.. or contact friends and family back home.. get an ally to get out.  Do you have anyone who would help you escape?  show up one day while he is at work and get you out of there?

It sounds like he is abusive on many levels.. I don't see much in your post about love .. 

Make your plans, but run, run, run asap.  You have a spouse that is abusive to you and uses you. And.... there is a kid that is pissing on everything when he is mad.  WTF?  Get the hell out!

You are being abused. Call your local crisis center. If you do not know it then check out https://www.thehotline.org/ tgey can help you.