Don't even allow the option. Tell them with all the preparations (or fib and say your house is already promised/booked for other family members) that you will send them some hotel or camping options.
Don't offer to help with the price of the hotel...if they can afford to take a 10 day vacation...they can afford a place to stay...if not...shorten the vacation to fit their budget.
Don't even offer a few days - make plans with others, go out of town.
Whatever you do - if you give an INCH, they WILL TAKE A MILE! It is a ridiculous imposition on their part, and don't play into it. Just apologize greatly and state you don't have the room, but would be happy to find some other options they can review - rent a camper, camp ground, hotel, motel, whatever (don't even offer your backyard for tents).
This is way too much to take on for anyone...especially someone who is hosting a huge event.
ADDED ~ Best Bet: Be proactive. Before she asks...Research local hotels, motels, campgrounds, church retreats (our family rented this church retreat in South Dakota for our entire family reunion on a lake, living spaces, private rooms and bathrooms) with lodging which is usually really cheap, and will feed families some meals if scheduled. Get a block of rooms at a clean affordable motel/hotel. Make the list up with costs and amenities, and send it out to a whole passel of relatives stating that "as much as you would love everyone to stay with you...it isn't possible, so you thought you would provide some options for those traveling from afar, since you are already booked up solid."
At that point if she asks, tell her you don't have the space due to other family obligations made, but luckily she should be able to find one of the options you provided to meet their needs..