I'd give them work - as much as necessary until they were too tired to bicker.
Mine are 12, 10, 4, and 2. The 10 year old is a girl - and that seems to be a source of contention for everyone. So when she and her older brother were fighting, they got to clean up their rooms until they were done being angry. My DH and I supervise. Now she and the 4 year old fight - I find cleaning windows more effective. One on each side. Talk to your 13 year old and help her to realize - notice I didn't say feel good about - that you have 3 children, and you love 3 children, and it's time for her to get over herself. Otherwise the next 5 years will be the scourge of your sanity.
Talk to your twins and make them understand that they must NOT intentionally aggravate their sister - that's stupid, and no, it's not necessary. At the same time, they're entitled to breathe, to play, and to make a reasonable amount of noise without her bellowing.
I think, too, it's time for you to stop apologizing. Your older child has no right to all of your time - neither does your younger. I think, honestly, if you started refusing to do everything by yourself (all the cleaning, all the yard work, all the dinner), they would find in the course of learning to carry their own load that it is easier to work together than to fight all the time... and you'd have more time for everyone, including your husband and yourself.
In short, kids fighting this much need work to do.