This is a tough one and I hate to say it, but you might be in for a rough ride, I hope you and your spouse have a strong relationship. You are dealing with a house full of adolescents & hormones. YIKES!!!
I would say that the first thing that needs to happen is a set down with the entire family aka The Family Meeting. I find that it is best if my husband (the step father of my teens) and I set down and talk first. We make a plan;
-What is the goal of the conversation?
-How will we handle and "tantrums" that might occur during the family meeting?
-When is the best time/place to do this? (I would suggest someplace neutral when the kids are all fed and rested) Not in the heat of the moment.
I also wonder, have you both asked the children what they like and don't like about the situation? It's hard on kids when they feel like they have no say, they're just being pull/pushed around with no voice to how they feel. Maybe some of the things can't be changed or adjusted but at least they will know they're being heard. This is a great opportunity for your children to get a lesson in conversation and the skill of expressing how they feel in a healthy way.
Start by stating the goal of the meeting and the rules, keep it simple, you can't tackle it all in one set down, this will take time: One speaker at a time, no yelling and no name calling. If someone needs to get up and walk away, let them. Let your children know that it hurts you and their father to see them so upset. Then let each one take a turn talking about how they feel about the current family situation. Keep any blaming or harassing in check.
I think a primary goal of your family meeting might be to first put a stop to the hitting/yelling/name calling. This is unacceptable and unnecessary. Once we start yelling/hitting/name calling then we stop listening and walls are built. It is much easier to listen and hear someone when they're calm and this is also a great lesson for your children to learn right now. You can't go to work and start freaking out every time your upset can you? No. They need to learn this and they are ALL at an age where they can learn this.
You can't force them to love one another, you can't force them to even like one another and I hate to tell you this, but as a step parent...don't get too hung up on them liking you all the time either. It's the great unkind reality of step parenting. However, over time and with trust, you can become their teacher and friend. Someone they respect and look up to.
You discipline your children and he needs to discipline his children. Your roles for one another are to be supportive and back one another up (and if you don't, never disagree in front of the kids, they will take advantage of this eventually) Set down together and pre-set consequences together so that you're both on the same page and showing a strong, consistent front when dealing with the kids. They need to know that you are a team, you are partners and you will NOT be pitted against one another. When my husband and I discipline the kids we discuss it privately then implement the consequences together. That way everyone knows what is going on.
IDEA: When my boys were in their early teens I got so tired of the fighting I just punished them both. I didn't care who started it any more, they were both feeding into it so they both got consequences. It didn't take long for them to get a clue and stop. They both learned to just walk away.
I would also suggest getting some books and doing some research on blended families. It's a trial and error thing but keep working at it and find what works for your family. You can't fix this with family trips and forced socializing. The issue is poor communication. If you can't communicate well with the people you're living with, you're going to have issues.
I hope that some of this helps and remember this is just an offer of advise from my own personal experience, I'm not at expert. We still have rough days and it's never perfect. It's so hard to blend a family, especially at the ages you are dealing with because they're all going through their own changes inside and out.