When you say you animated the door, I will presume you mean vertex animation. This would create this collision issue.
The collision model created for any object is an exact replica of the object which is rendered, except much lower polygon count. This collision model will not change, and is static. If you animate the model with vertex animation and change the shape or position of the model, the collision file will remain in the same position and same size and shape - this fits in with your car door problem.
The way around this, is to either, create a custom collision model, which is very large, such as a cube or cylinder, and use this as a collision model. The animated object should then be within the collision area - however this is not an accurate representation of the model.
The second method would be save out your model in the finished position of the animation, and create a new static object and collision file - the swap out these objects once the animation has finished playing.
The last method, would mean being clever using markers in TW. You could rotate or move an objects position from one marker to another. This will actually keep the collision file in the correct place, as no vertex animation takes place.
Just quickly, the future roadmap would be for objects to use bone animation, just like characters do. This would be much cheaper in file size, easier to animation objects, and also have dynmaic collision.