If that is the way he thinks then you should "charge" him for child care. He should be paying you half of what it would cost to put your DD in day care.
I agree, but really he should be paying you what an in home nanny or au pair would charge, since they provide a different level of care than a daycare center, and much more on par with what the OP is doing. Heck, I know for a fact that if you have an au pair you are expected to provide room and board as well as spending money and a chance for her to get out on her own as well. You can't have the au pair show up and then demand rent and half the electric bill.
I would be really annoyed too about the stepkids, as well. They are definitely part of the family and need to be treated as part of the family, but I would be very annoyed that "I" have to be the one to find a way to provide for them. Providing for the stepkids and birthdays should be something you guys pay for together, or something that he pays for himself.
I was thinking the same thing but couldn't come up with a nice way to phrase it. I'm so glad that you see the stepkids as your kids but when it comes down to it, exclusive control of spending on them, if it is going to come from someone, should be from your DH and not you.
I'm really sorry that you are in this position. You two are long overdue for a chat about family finances and what you want out of life. Do you want to be a SAHM? If he feels the same way, he needs to pick up the financial slack. If he is insistent on the whole your money, my money thing, well, you'll have to go back to work but let him know that he will be chipping in towards the expenses that come from that.
I can only compare to my own situation and it just doesn't seem right what you are going through. I haven't worked out of the home since I went on bedrest during my pregnancy with my oldest 8 years ago. Two years ago my cousin came to me and asked if I would watch her kids, I said yes. I have to say, I felt really good about making a contribution to the family finances. Really good, it's made a lot of things easier and some things more possible than they would have been- a lot of little extras.
Anyhow...... I lost my job two days ago. A week from now I will no longer be working due to cousin being downgraded to part time at her work. I've really been beating myself up about it, OMG, what will we do, that's the money that was going to make it possible for DD to go to camp this summer, pay our vacation, etc....
DH, who has the most reason to be upset about the loss to family income (because anything that comes in belongs to the FAMILY, not the individual), has been the most supportive.
He keeps reminding me that it's not my fault and that
my most important contribution is the running of our family. I can only imagine you are doing many of the same things
Honestly, it was very nice to hear but he pointed out that he is able to relax and do his job well because he knows things are running well at home. The kids are well cared for, they are always picked up from school on time, they are having nutritious home cooked meals, and a million other little things that just get taken care of and he doesn't have to worry about. He knows that there will always be groceries in the house, that there will always be a birthday card sent to a relative, that if he gets caught up at work and gets home late that the kids are okay (if you're late enough, daycares can call the police to get your kids

).
He said that the peace of mind of knowing everything is cared for at home is really what my job is about. I had never really thought about some of it before, or realized that he realized just how much I do. I'm pretty sure that you are doing many of the same things from what you mentioned- planning birthdays and holidays and whatnot. I'm just really sorry for you that your DH doesn't seem to see and appreciate all that you do.

I hope you get it all worked out.