Hmmm.... I think I don't understand you

The "earth" rotates around the sun... but with the rotation of the sun? Is this correct? Like a, lets say mountain on the earth?

It's all the same... No matter if things are "welded together or not.."

You know the position and rotation of "sun"... You need to know this, because you want your earth to move there and rotate exactly the same...

So what you need to do is:

ClearWorldMatrix;
Rotate matrix with SUNs rotation
Translate Matrix to suns position.
draw sun
ClearWorldMatrix;
Translate Matrix to the distance earth has from sun
Rotate matrix with SUNs rotation
Translate Matrix to suns position.
draw earth