I think gingerbread can offer you a subsidised 'nanny' type service in certain circumstances. Also you should contact your local surestart centre and your health visitor for advice and help.
Don't waste time, energy and your life trying to make your ex be something he's not. Get on with your life and find your own solutions. If he's around that's a bonus FOR THE CHILDREN, but certainly don't rely on him for anything or expect anything for yourself from him.
The idea about going out and leaving him to the kids when he does come over is a good one.
You also need to ask for help. If your mother is offering not much support anyway then you've not got much to loose by making it clear you need help and if it's not going to be family that help you are going to be calling on outside organisations for that help in the very near future as you are very quickly going insane. Don't know if you are, I certainly did for a while though and I only have one child!
Tell your mother you need help and tell her exactly what you would like. Ie could she at least treat you and your sister equally and have one of your children overnight once a week too. Or could she take 2 or three of teh older ones to teh park for an hour, or help you out on a trip to the park with them all.
Also wondering why can't you claim any government supportat all? At the very least you should be entitled to Child Benefit. And if any of the children are over 3 you should get some free places at a playgroup or nursery. Also nurseries and playgroups sometimes are able to get funding for needy children and may be able to get you a subsidised place. You won't know until you ask.
If you have redundancy money which is fast vanishing then your situation might have changed significantly enough to start claiming Income Support. Don't say 'I'm not entitled to anything', find out for sure. Bear in mind the government expect you to ask, they don't tell you what you are entitled too. So ask someone who knows, like CAB, gingerbread or Surestart.
Surestart are there for families with younger (preschool) children. So if I were you I would make t hem my first stop.
best wishes
Gilly