I agree. That's not a play date, that's childcare.
I would be uncomfortable too, watching a child I know my charge doesn't get along with. So if she says no, MB needs to respect that.
Can your son go to the other boys home? Or are his parent working so they are hoping for free care from your nanny? 8-6 is a long day. If nanny agrees to that, the boys parent should absolutely pay the nanny for it.