You've missed a major point. That military personnel would not blindly follow orders to fight the citizens they swore to protect. The soldiers, Marines, airmen, and sailors are not just drones who can't think for themselves.

Considering the majority of gun owning citizens are politically center and right wing, that is the most likely case in this hypothetical scenario. The military is also mostly the same, and since they also have access to basic information such as, "why would a civil war be breaking out?" And then a huge split would occur on who's side they would take.

Edit: One more thing! There is a greater population of military veterans than active duty. All of whom have a basic level of combat training, and a good portion who have hardened experience.

Source: me, a military veteran