I think your DD is acting ridiculous too, and it sounds like she is jealous. I think it's great your DS is getting out and taking his older children deer hunting. Maybe people here don't realize deer season (rifle) here only lasts 10 days, so it's not like he'll have a chance to take them deer hunting later. And after two months on the road, he needs a hunting trip with his older kids to relax and unwind.
I don't blame you for not wanting to keep all three little kids at the same time. That is too much! Your daughter has two weeks to find a babysitter for her two children, which should be plenty of time. Keep your chin up and don't let her get you down. You're doing the right thing. I'm glad your son is getting to spend some time with his kids after not being with them for so long.
Nobody NEEDS to deer hunt. The son NEEDS to spend time with all of his kids not just his kids from his marriage. The son HAS two weeks to find a sitter for his son he is not spending time with. The son has plenty of time to find a sitter, maybe try the kid's mom!