Should Space Command be another military branch or managed by the Air Force?

Managed by the Air Force.

We could wrap Army and Navy Space Commands into AFSPC (which I always thought was a good idea anyway) and they could continue to manage satellites, launch operations and the Theater Missile Defense as a branch. There is your Space Force in a nut shell. Once we get another space transport system they can roll that in as well.

I don't know, and I don't think they do either.
My concern is that the Space Force gets treated like a red-headed stepchild when it comes to procurement like the Dept of the Navy treats the Marine Corps.