If I use the Earth as my point of reference on a model, would it be valid if I said that the Sun orbits the Earth? (in my model) What the title says.
If I create a model, and I use the Earth as my point of reference, is it valid to say that the Sun orbits the Earth inside my model? Or is claiming that invalid?
 A: It depends on the level of rigor you want.
The Earth does not actually revolve around the sun.  It revolves around the barycenter of the solar system.  This is a fancy word for the center of mass, and it turns out that the barycenter of the solar system is slightly outside of the sun.
If you were to try to characterize the motion of the sun in an Earth based reference frame, you would find it wobbles, as a result of the compound motion of the Earth around the barycenter and the Sun around the barycenter.  Whether you consider such trajectories "orbits" is a semantics question.
As an interesting comparison piece, consider the path taken by the Hilda asteroids, which are locked in a 3/2 resonance with Jupiter.  We can play the same game, declaring our reference frame to be that of Jupiter, and ask "are these asteroids in an orbit around Jupiter?"  Well, regardless, their path in Jupiter's frame is quite complex!

When some people talk about orbits, they're only talking about Keplerian orbits - circles, ellipses, parabolas, and hyperbolas.  Go to a higher level of fidelity, and no orbit follows those trajectories.  There's countless effects that lead to other shapes (other gravitational bodies, drag, etc.)
And, of course, if you get into deeper mathematics, like dynamic systems, we find "orbit" just describes any trajectory, and "periodic orbits" becomes a useful term.  That's clearly not the sense of "orbit" that you are looking for, but I can say that the dynamic systems definition personally threw me for a loop until I find out they weren't talking about what I thought they were talking about.
A: You are talking about the geocentric model and that model has very complicated orbits of planets around the earth. Here have a look at the orbits of planets around earth:

So why not just use the simpler one in which all planets revolve around the barycenter of the solar system. 
Also a point to note is that a model with earth at the center of the solar system is not inertial so Newton's laws of motion wouldn't work without a centrifugal force which only adds to the complexity of the case. 
