I'd be surprised if your sister is entitled to anything. The threshold is very low these days.
My DD goes to wrap around clubs at school every day. I work full time with a very demanding job and sporadic support from EXP. Leave house at 7.30 every day, back after 6. The school holidays and (bluddy inset days - who's idea were they?!) are a nightmare, so at least your sister won't have to worry about that.
It's obviously up to your sister... only she knows what she can cope with, but at aged 8 and 12 her kids are only going to want to be more and more independent anyway, so if money is an issue she should probably stick with it at work.
It can be overwhelming at first, but it'll all work out. I've worked full time since DD was 10 mths old. It was that or lose my house. I do feel cheated and want to punch the smug married SAHMS who tell me how bored they are and that they don't know how I do it and how perhaps they'll find a little voluntary job next year (yawn).
Sorry that turned into a bit of a rant, lol...
Sadly OP, this government delights in pushing women out to work, but anyone with a semi decent job gets no benefits or support.
And single mums sadly get the worst deal in my opinion. Dad's who won't pay and a system that doesn't help 😕