I'd spend my time getting her trained up in exactly how you like your cups of tea etc! I remember DH going back to work when I had ds1 and the amount of times I sat down to BF with no drink, my phone left in the kitchen or the tv remote just out of reach was infuriating! She could prove to be a great little helper.
It's not always as simple as everyone makes out regarding step parents 'not providing free childcare.'
The child and her mum need some kind of schedule and can't be held to ransom by a random shift pattern.
The op and her husband share a household that presumably needs his income, he can't just ditch his work or risk getting sacked for being unreliable, especially now when there will be a huge queue of people lining up for jobs!
In an idea world the dad would be there for all the contact time, but I'd love to meet anyone who lives in this perfect world.
The way you phrase this will be really important, you clearly like your DSD and are worrying about how you will cope in your first week alone, that's perfectly natural.
I think if altering contact doesn't work I'd at least get your partner to try and arrange some flexi time so he can do the school run. Will she still even need taking or is she moving up to secondary and can get herself there?