I think that, sadly, her inability to split her pack of kids is the real problem. If you can't host her whole brood, then your son will not be able to play with his friend outside of school.
While it's awkward, she's pushy and rude. Say, "I'm sorry, but no. I can either take the older boy, or the boy and the girl, but I can't take all three. If that doesn't work for you, the children will just have to play together at recess."
I'd watch this one for birthday parties, too. I bet she tries to drop off all three.
If your son is upset about it, simply say, "I'm sorry, but we can't work it out for you to see your friend after school."
My DD has asked for playdates and I've ventured to ask but not all of them pan out. There's one girl I won't even ask about because while I like the kid, the mom is...high strung. No way would that work out well. I focus on other kids.