Dearest Burnt,
So sorry to hear what a hideous time you are having.
I think the children whinge and whine because they have a very unhappy mother.
I wonder if you could use some of the £50 a week on a cleaner and just use the dryer to dry the clothes anyway, regardless of what your horrid, lying unsupportive and now abusive H says.
That shopping bug you have - it fills the desperate empty hole in you doesn't it? (I have had it too, a long time ago) It also brings you some feeling of control in this awful situation where everything seems out of your control. But you can get that feeling from other things, like squirrelling away that money for things that are really important to you - a cleaner, a taxi, a gym visit, a private one to one counselling session.
When you say you can't eat because you are sick to your stomach, I think about all that fizzy diet coke that's going down and worry that with the stress and all, this diet coke habit will give you a stomach ulcer. Also, you mentioned being an anxious person - well that diet coke is full of caffeine as others have mentioned, and this amount of caffeine is going to seriously affect your anxiety levels. you must be absolutely buzzing with it!
Please go and see a doctor or a personal counsellor and get yourself some help.
Once you are in a happier place, your children will be too and when they do whinge (which will hopefully be less), it won't bother you so much because you won't be so hyped up on caffeine and you will hopefully feel calmer.
As for the husband, well I suppose you have to decide if this is what you actually want to do with your life...
If it was me, I would rather be without him, and lead my own life with him paying maintenance and me controlling my own finances. If he earns £52,000 a year, he would have to give the lion's share to you to support your children.
Best of luck with sorting things out for a better life for yourself and your children.