Very similar to ideas I've contemplated, but I have a different theory on the Lucifer.
I tend to think of the Shivans as the vacuum cleaners of the Universe, much as is contemplated at the end of FS1, but also as a species in its own right.
The real conundrum around the Shivans is the singleminded destructive desire of the Lucifer fleet, versus the odd behaviour of the Sathanas fleet. I see the Shivans as an ancient race that seeded systems of the universe with dormant fleets designed to suppress advanced destructive species so as to preserve struggling life forms on other worlds (that much I derived from FS1). The Lucifer came not from a mysterious node or rift in subspace but lay dormant in subspace itself within the Ross 128 system, and was triggered by Terran-Vasudan actions (which we don't know terribly much about prior to the FS1 intro video).
In contrast, I think the Sathanas fleet contains the majority of Shivans who make up the Hive mind, a majority that were isolated from their home systems after some cataclysm. I think they've been utilizing the Knossos portals constructed by the Ancients, but are themselves cut off. Furthermore, I think the destruction of the Capellan sun was an attempt for these ships to move across systems, perhaps even galaxies - an attempt they failed in previous in the nebula beyond gamma draconis.
Here's the interesting thing that struck me a while back - Capella was/is a binary system. The nebula was a binary system (now it has only one sun). The area beyond Knossos 2 is a binary system. Now, the presence of Knossos 2 suggests that the Knossos in Gamma Draconis and the one in the nebula were constructed after the original sun in the nebula went nova and created the nebula. Knossos 3 is in active use by the Shivans, so they don't want to wipe it out by toasting a sun. Capella is the logical choice - create a supernova, but preserve some gravitational arrangement due to the momentary presence of the other sun, allowing the Sathanas fleet to enter subspace.
It's conjecture, but I think the binary nature of those systems is somehow important, and the sathanas fleet had entirely different objectives from the Lucifer (and different technology) implying the Lucifer is older and has a different overall purpose.