Want to add an anecdote -- my new stepmom changed the locks when we kids were teenagers and did not give us keys. Most of us were off to college by then, but the house was the family house in which we grew up, and at least in my circle of friends, everyone had keys to their own family house. She couldn't have made it clearer that she wished we kids would just dry up and blow away if she had posted a sign on the front door.
Let the boy live as he has lived. You *are* the newbie, and you will win in the end because he (the child) will be leaving in a really short time. Let him cuddle, and lay out his clothes in his dad's bedroom, and talk to his dad in the morning. As I said, he'll stop soon enough, but in the meantime he will get so much from being with his dad. And presumably you, if you let him be included.
I'd put on a nightgown and encourage the snuggle. Soon enough the kid won't want to snuggle with his dad, and his dad will miss that closeness even if you don't. It's sad, when it leaves. It's nice that the kid refrains from "accidentally" kicking you when he's bonding with his dad. At least he wants you around enough to keep from being annoyed that you are there. Don't be the instrument of elbowing the child out of the way, especially when he's at the last cusp of his childhood. That is a very sweet time and he'll never have it back. You'll have tons of time with the dad, years and years if things go well. Give the kid this last bit of rainbow land before reality comes along in the form of teenager years and destroys his sense that the world is secure if he just can cuddle in the morning with his protective parent.