My parents usually start going at it by day two without any outside provocation, just the increased commotion of visitors.
I'd suggest Sunday brunch would be a wonderful time to see your parents. If my parents were "begging" me to stay with them, I would take it as a sign that there's already waaaay too much drama for me to even consider sleeping under their roof. Not a chance! My response would be (and has been when the issue has arisen of where to stay during visits), "I will stay where I feel like staying and I am welcome, and I will tell you where that is when I decide." End of story.
How long are you going for, by the way?