Ok, yes if she was separated then she would be classed as a single mum. These are the benefits I think she would get...
Child Benefit: £20 a week
Child Tax Credit: You would get about £60 a week on a yearly salary of £19,000 and would go up for less earning
Working Tax Credit: not sure how much it would be but if she is working less tahn 16 hours a week she would qualify
Housing Benefits: you can claim housing benefits towards rent only, not towards a mortage. You may be able to claim for help towards mortgage payments but would need to speak to the welfare rights department of the council
Income Support: probably able to claim this on working such small hours and if claiming this then you have more entitlement to housing benefits
Spousal Maintenance - not too sure what this is but if they have been married a while or he is rich ( ) then she may be able to claim
Child Maintenance - is (I think) 15% of the fathers earnings
Please dont quote me on any of these, this is just what I remember from doing my research as I am in the same situation as your sister. The DWP website has calculators on that you can use to work out eligibility.
Hope that was useful!!!!