How old are her DC's? If they are all 5+, then she will not be able to claim Income Support, but she will be able to claim Jobseekers Allowance.
The reason her Tax Credits will have been reduced once she was no longer working is because there are 3 separate 'elements' to Tax Credits.
First there are Child Tax Credits. You get these whether you are in work or unemployed.
Then there is Working Tax Credit. You can only claim this if you are working 16 Hours or more a week.
Then there is the Childcare element. Again, you can only claim this if you are in work of 16 hours or more per week, and it covers UP TO 70% of your Childcare costs. (hasn't been 80% for around 5 years!)
The reason her Tax Credits have reduced is because she is no longer entitled to the elements that you can only get if you are working.
If all your daughter'a children are over 5yo, then she needs to claim INCOME BASED Jobseekers allowance.
If her youngest child is under 5yo, then she needs to claim INCOME BASED Income Support - she may have been told that she is not entitled to IS because they may have been looking at contribution based IS.
Also, the amount if savings your daughter (and her children, added together ) has will make a difference. If you and your DC's have savings of over £6000, you will be expected to live off that for a year.