can you ask your local childcare centre if they do occasional care... as a lot of them will.
I know mine does.

I do the same as you - put dd in for socialisation and i just do the housework and have a litle me time at home 1 day a week but it is a booked spot so i have to pay for it every week regardless.

HOwever if one of their kids are sick they have an opening for occasional or emergency care.. it is worth a try.