Hi bedsidedrawer I'm really sorry to hear you are struggling, you are not alone I'm sure and I too have had many a long rainy school holiday struggling so know a bit how you feel. You sound like a very good loving mother who is having a very very rough time and you've obviously had things going badly for a while to get to this point.
Have you spoken to your doctor about your feelings? I think you should seek some help there esp feeling rage and depressed. (although to some extent these feelings are normal, it's just if you think it is getting overwhelming) It sounds like you really need a bit of respite for a few hours a week from somewhere, easier said than done I know. Also would you consider looking at local churches and seeing if there is anything on there for yourself or the children.
Please don't think that being a SAHM is not a job it's a career (!) I would say and sometimes amidst all the drudgery it's hard to see it that way but honestly raising 4 humans you are doing the most important job. That's not to say you shouldn't look for some other work to fit round your life it's just that I read so many mums saying that they feel worthless just being a mum ...there's no 'just' about it.
Facebook..... again, this can be a real confidence and morale crusher when you see others posts of their holidays or whatever. I don't look at it, people are just showing off the seemingly best bits of their lives, you don't know what else goes on. I don't think it does any good to judge yourself on what others' lives look like. You know someone could be looking at you and thinking 'lucky woman she has 4 lovely children'!
And children don't need our attention (other than obvious safety stuff) and to be entertained (have money spent on them) all the time, this seems to be a modern way of life but honestly children do not need to be entertained by adults all the time. They have strong imaginations and can entertain themselves more than we realise.
Hope you get some help Bedside, and can soon get back to what you were with some positivity. 