HP, I truly hesitate to ask this.... but.....why is it you don't have a consistent parenting schedule? As in, it's the same every week, or follows the same pattern every two weeks? Is it a work schedule thing, or you are just trying to be nice to W by allowing her to choose every so often? Uncertainty about living arrangements? Something else?
I, my H, and my D12 can tell you where she's going to be every evening from now until mid-March, with a pretty good accuracy. The schedule is set, it's on the family calendar app, and for the most part H and I plan around it. I will take D12 any time H can't, but it's only happened once, and I've never asked him to cover a night that's mine.
Is your W resistant to that sort of arrangement? Are you? I'm not suggesting at all that's what you need to do, it totally may not work for you. I'm just curious how you got to what you are doing now.