@Babyice
I think the best thing to do is to speak with your CM and find out why she sees the arrangement as problematic.
Perhaps she just feels uncomfortable about taking the money when your daughter is absent, but equally can’t do without it, so she’d rather fill the place with a more regular attendee?
Maybe she finds the erratic attendance disrupts other children in her care. They do get used to each other and often form friendships. One of them might spend days looking forward to seeing your daughter, and be very upset if she isn’t there.
It could be that your CM feels she needs a certain amount of time in order to properly assess and plan for your daughter's learning and development.
There are cases of Ofsted inspectors downgrading childcare providers in this sort of situation. Some inspectors quite rigidly believe you can’t do anything for a child who attends one day a week, irrespective of the parents' needs. Remember, Ofsted’s ideal is based on state schooling, in which you are coerced into attending five days a week. A lot of settings, especially nurseries and preschools, simply won’t take a child for fewer than two days weekly.
Not saying this is necessarily the case, but these things are all possibilities. A chat with your CM might just clear things up. Hope you find a way forward.