S.R.
Oh mi..the stress can put us all over the edge.
I agree that I would treat this as sibling riveraly and treat the visiting girl the same way I would treat my other four children. Also, it is important to remember what the little girl is missing by not being at home with her mom and her toys.
I would take the play time out of your son's bedroom if that is where it is. You might want to invest a little money into Little People or a few Barbies. Give the girl you are babysitting her own toy box and keep it in the living or family room. Your little one might be more willing to share (if he is like my 5 yo) if he is getting something in return (being able to play with her toys). Your son might feel like he is loosing everything and not gaining anything, where the little girl might be feeling like she doesn't have anything of her own to play with and has to play with all the boy toys. You might also want to talk to her mom and see if her mom has toys at home that she doesn't play with very often that the mom would like to bring to your house for her to play with.
Also, throwing in the towel and not babysitting any more will most likely cause the same amt of stress, just in a diff way. Such as not as much income, not as much fun money, lonliness for your son. I also LOVED the idea of giving them BOTH chores. With my children, and their friends who spend the night, when they are fighting, I put them to work. Idle hands are the Devil's playground is what I tell them. And I also tell them once they figure out how to get along and get (for example) the kitchen cleaned they can go play Barbies some more. Best of Luck!