It will be a nightmare to track, and you will be dependent on the other family agreeing that times are correct. The easiest way to do it is to have a sign in/out sheet or app and nanny sends you the week’s total at the end of Friday for payroll.
How do you plan to handle overtime? Nanny gets overtime for anything over 40, doesn’t matter which family uses the time. So, if the nanny has child A for 8.5 hours Monday through Thursday, then overtime starts after 6 hours on Friday, even though it’s just your child.
You may want to consider each paying $11-11.50 per hour for x hours per week (if you are set of a range of $20-23 for 1-2 child rates) to guarantee the full schedule, and guarantee that whole time. So, most likely that would be around 45 hours, say 8-5 m-f. Doesn’t matter if the other child is there Fridays. Doesn’t matter if you pick up at 3 every day. You’re guaranteeing that the nanny is available for the entire 45 hours every week, and you’re guaranteeing that she is happy to stay with your flex schedule versus finding something more consistent.