Hmm! Sometimes people and animals in dreams are parts of ourselves seen as if outside us, other times they are people in our environment.
A fox is wily, dangerous and cunning. In your car dream, the vehicle is you. The fox was strong and muscular, and appeared suddenly from the ground. In the other dream, it was also just there suddenly in the room.
Is there anyone in your life who you're wary of? A rival or competitor? The dream sounds to me like an enemy suddenly appearing on the scene, someone plotting to 'outfox' you. (Not necessarily in the future, dreams can reflect how we feel about what's happening now).
You wanted to shut the door, but felt awkward as you were a guest. Maybe this is saying that you should think about taking steps to protect yourself against ambushes from this person, but you are reluctant to do so, because it would look rude, you have no right, "it's not my place." But if you don't, then it will indeed cause you upset!
If I had that dream, I would try to identify who the fox might be.
I hope that helps.