I know a reasonable amount about sickness benefits and could help you think it all through if you like?
It sounds like your sil will be entitled to Disability Living Allowance. A word, or several of warning, the form is hell, they reject a lot of applications only to grant them immediately on appeal and it's very, very slow. I would make it your first priority to get this form requested and started. If this is your first foray into benefits I really would go to the CAB for advice filling it in.
If your sil is of working age and has made NI contributions then I think she'll probably also get incapacity benefit.
Depending on what rate of DLA she gets, any savings, other income, she may get income support to top-up the amount of incapacity she gets in order to meet the amount of money the law says she needs to live on.
If one of the children is likely to end up doing a lot of the caring then they could get carers allowance.
If she goes onto income support then Council tax benefit and housing benefit will come into play also. Remember these are dealt with by the council usually - not the benefits office.
dwp.gov.uk
direct.gov.uk
jobcentreplus.gov.uk
are all good - and can give quite detailed information if you've got time to hunt.
Most of the forms you'll need can be downloaded from those websites.
Hope this helps.