If you are paying driving time the same as work time you could do it like this:
Calculate drive time from point A (office, supply room, cleaners home) to point B (appointment address) and back to point A and include it in the actual appointment. So let's say your cleaner Mark has an appointment scheduled from 9.30AM until 11AM, and he needs 30 minutes to go from office to appointment and 30 minutes to go to another appointment. In this case, you could just add 1 hour to your actual appointment, and make the start time of this appointment to be from 9AM and end time to 11.30AM.

If you are paying driving time the same as work time you could also do it like this:
Create a new fake customer called Work Shift and use it to create a fake appointment for this customer every day. The cleaner can clock in to the shift and also clock into their real appointments so that you can track how much time was spent cleaning. At the end of their day, they clock out of the Work Shift. On payroll, you will only pay for the shifts called Work Shift since they include the time spent cleaning and the drive time.

If you are paying different rates for drive time and work time you could do it like this:
Create a new fake customer called Drive Time and use it to create a fake appointment for this customer every time you need to include drive time in payroll. What is important here is to assign the right cleaner to this fake appointment so you could find them in the payroll, as well as to adjust the hourly wage for this fake customer.