As a registered childminder, you are a registered childminder only when minding at your own home (to my knowledge) - after all, your registration certificate states the premises address.
So, if you are working in the home of the children, then that would have fallen under the old Home Childcarer scheme (which is no longer in existance). The scheme has been replaced by CAS (Childcare Approval Scheme), which you would need to register with separately to your Ofsted registration I believe. At the moment I'm on Ofsted's system and on the system run by CAS... it's a pain in the bum and WILL change at some point over the next few years, following the introduction of the Childcare Act 2006. (At least, that's how I understand that Act currently, Ofsted will have a List A and a List B).
So, moving on to your precise questions.
Insurance - you will need to check your existing policy to see if it covers you, it might, or it might not. If it doesn't, then Morton Michel do a Nanny policy which would be suitable.
As a single parent, your employer MAY be able to claim back via Tax Credits, if you are registered with CAS (see above) as you are caring for her children at her home.
However, as a Registered Childminder, you could care for the children at YOUR home, and thus she could then claim via the usual method as you are registered with Ofsted.
The thing you haven't asked about here is your Employment Status... as it's likly to change!
When you care for ONE family only, and care for the children in the family home, you are not a Childminder - thus are no longer Self Employed.
As the care is Full Time, I highly suspect you will be classed as an Employee, so your employer should register as an Employer, and make deductions on your behalf for your Tax and NI (plus pay employers NI).
Oh doesn't this all get rather messy. Is she SURE she doesn't want you to care for the children at YOUR home... surely that would be the easy soluition.