In your shoes, I'd do the following, but it depends on your budget, of course.
I'd start by saying
I'm looking forward to having you in the area and spending more time with you and our group of friends.
Unfortunately, we've had a recent death in the family and things have been very unsettled and stressed for me because of that. I'm still trying to work through details and handle everything on my end. Therefore, it's unfortunately a bad time for us to have houseguests and I cannot offer you a room at my house for the near future.
I don't know how close you were to the relative who died (my condolences, btw) or if you were involved with any funeral arrangements. Nevertheless, it takes a toll and it sounds like you've been exhausted and need to wind down. I'd focus on the death part and not the "I need relaxing time" because it's something more people are likely to be understanding about and it won't ruffle as many feathers.
And then I'd add
However, I would like to offer to put you up in a hotel for three days <maybe mention the type so it's clear it's not expensive like the Ritz> and meet up with you for coffee or dinner sometime.
Please, let me know if that works for you and I can make a reservation for you at X hotel.
If the hotel is out of your budget, then offer to take her out for a nice meal after she's been settled for a while and you've had a chance to destress and relax for a week or two. Obviously, you want to keep things on good terms with her and the rest of your group of friends.