Itati - first of all, you have three kids. You are outnumbered and to be admired if you can keep going at all! I take my hat off to anyone with more than two who stays sane.
Second, things always get worse at this time of year in our house. Just when I think I should be enjoying summer the kids get end-of-term-itis and drive me up the wall. I know that the beginning of the holidays is often bad too, when they get beginning-of-term-itis too.
There are things that you can do.
I found reading Siblings without Rivalry helpful too. Some of the strategies work, but also it reminds you that you are not alone and that other people are dealing with chaos at home too.
I also found reading 1-2-3 Magic really useful. I have a copy here, which you are welcome to if you cat me.
This morning, before we murdered the kids (and we only have 2) I quickly started my reward book up. The kids have ten stars each. If they transgress, they lose a star. If they do something nicely, they win a star. I usually do this for the first week or ten days of the holidays, but dig it out if things are wobbling.
I find it helpful if I jot down what they are winning/losing stars for. It helps me to see what they do well - it's easy to believe that they aren't doing anything well at times - and to see if there are particular patterns in what is going wrong. EG if "Being rude to mum" crops up twice a day, then there are double stars on offer if it isn't there tomorrow.
Finally, you sound really low. Do you need to go and have a chat to your GP? Or to your dh? You are the main carer, and you need to be OK. Make sure that you are getting some you time. When did you last have a girls night out and laugh a lot? Are you getting enough sleep/chocolate? Never mind the kids for a moment. Look after yourself. And keep posting.