This sounds like you'd be her nanny then? Are you doing this in her home or yours? I'd be inclined to ask to do day shifts at your place and the evenings at hers. if you have a spouse who could pick your son up after a play date and take him home for his bedtime routine while you stay at your friends house and do bedtime routine with him.

What do nannies charge where you are? Will you supply food and milk?