I am a little confused. So she is paying you full-time but only using the spot part-time? why can she not use days she is paying you for? Are you not open the times she is wanting to drop off?

IMO if she is paying for a full-time position then you should be open to her on a full-time basis during the full hours you are open. If you open early for her then I would say no your start time is your start time for all.