Personally, I charge by the week.
Infant care is so hard to find here that it's just one flat weekly rate regardless of how many days they need/use.
I think you should always charge more (when broken down) for part time care verses full time.
Doing that would eliminate your need to fill odd vacancies such as Mon/Tues only. Who ever is using the other 3 days is getting a good deal as programs here that do allow part time separate it into M/W/F or T/Th spots only as they are much easier to manage than two random days.
That was a lot of rambling on my part but I guess I have no advice as I don't offer care like you are doing...I am confused enough with any kind of math so I wouldn't be able to make that work. Sorry.