If you ever hear the "well my mom lets us do this..." Inform them this isn't their mom's place and that that's not how things work here. Then enforce it. NEVER give leeway just because "well mom said." Because mom isn't an adult in your household.

Have you asked him why, if she is so great and he clearly prefers how she does things, why he doesn't pack up and go back to her?  He may not realize how he is coming off to you.  Or he might and the answer may be that she has moved on and he is making do.  Either way, it is a reasonable question to ask and may give you the information you need to make a decision.

He's acting off of guilt that the step kids are not always with him so he feels he needs to over compensate and make up for it in some way. You get the sh!t end of the stick because you're his wife and he feels you should understand, but that's not how it works. Ask him to attend therapy to address these issues and how you don't feel you have value in the marriage because he dismisses everything you say and do.

Also, as a poster commented when the kids say "that's not how my mom lets us do it" you tell them different house, different rules, and this is how we do things HERE. If they refuse to listen I'd wash my hands of it all and let your H handle EVERYTHING when it comes to them. From the meals, to the laundry, to dropping them off, whatever it is he'd have to do it and I'd have no parts of it.

You have your own kids to take care off, why get frustrated and lose your mind over skids that could care less what you say or think. I'd rather focus my energy on people that care and where it would make a different. Since you and H are not on the same page they will not respect or listen to you until he sets clear boundaries.

This is really bothering you and you need to get to the bottom of what you are going to do. Prolonged stress has horrible effects on your health; both mental and physical. 

Not only are you troubled because you feel like your husband isn't letting you parent how you want, but he is letting things slide with his kids. If this is true, your bio children will notice when they get a little older. 

I'm sorry you are going though this, but if you can't work this out with your husband, you AND your children might very well be better off without him. 

I think you both are at fault and you both are doing your own brand of guilty parenting.

On you, you referred to your daughter as "your best friend". My guess is that the guilt of all the change in her life, which I am sure brought out negative emotions, mixed with you relying on her for emotional support when you were single causes you to be far more lenient with her than you realize. Yes, young children need compassion, but they also need guidance to understand that all because they have a negative emotion doesn't mean that it's catastrophic. I am going to make the assumption that you baby her, and it annoys your DH just the same as his lack of boundaries with his kids annoys you.

Regarding your DH, I totally understand why his behavior bothers you. I deal with nearly the same situation - down to BM needing Tylenol while getting herself a new tattoo. However, your DH's failure comes from being guilted by his kids because their mom cries poor. You aren't wrong in expecting her to chip in for clothes and school supplies, or wrong in expecting him to enforce that. The kids won't stop crying poor themselves until Mom does, and your DH setting boundaries with her will help that.

My next steps would be the following:

1. If you don't have a child support order for your daughter from her father, get one. If you don't have one, it is unfair that your DH pays CS for his kids and then also helps supplement yours, but your daughter's father doesn't help her financially yet you harp on DH for paying dor things for his kids. That breeds resentment at a level your DH may not know he can even breed it at.

2.) Take some parenting classes for blending families with your DH. You both seemingly have a lot to learn, so learn together.

3.) Find a counselor specializing in blended families that can help you two communicate. You are both right and you are both wrong. I don't think either of you have the skills to communicate your issues effectively without getting defensive.

4.) Remember that he is a stepparents, too, and a full-time one at that. Your daughter will annoy him just as much as his kids annoy you, and he gets even fewer breaks. You're going to HAVE to be harder on your daughter than if you were single because his threshold for her is going to be lower.

5.) Disengage from anything affecting his XW. If your bills are getting paid and he still has money left over that he wants to spend on  his kids (within reason), let him. As you start making the full weight of her actions hit him, he'll likely get fed up faster. Mix that in with some therapy, and he may be able to actually set real boundaries.

I think you both have fixable issues, but you both are going to have to realize that you both need to change.

What are you getting out of the relationship other than stress and anxiety, and having to treat your daughter in a way that is not what you'd naturally want to do?  I'm not  a big fan of counseling, but especially if you have anxiety that is coming up now, I would find someone to talk to about these issues.  You need to stand up for yourself.  If your husband is walking on eggshells with the skids and his ex-wife, then you're not making it painful enough for him to choose to cater to them instead of to you.