I'll grant you that these militias are well-armed and have sketchy loyalties, but if the US military decided they were honor-bound to defend the Constitution, against Trump, they'd crush the Oath Keepers and their ilk.
Many of the members of those militias are themselves military or ex-military. Which already tells you volumes about how likely it is that all of the US military would "decide they were honor-bound to defend the Constitution". Besides, those guys don't think of what they are doing as contradicting the constitution - quite the opposite! They are very obviously wrong, but that has never stopped fanatics from believing in their creed.
The real question, anyway, is not whether the military will obey Trump's illegal orders, should he issue them. It's whether the military would do something to stop the militias if Trump lets them off the leash with an explicit mandate.
And my concern is that most of the lower-ranking officers and people below them will prefer to sit it out. Because if they do something, and it's not enough, they are all looking at actual treason charges and likely death sentences.
Do you really believe that these lower-ranking soldiers are going to sit idly by while they watch their family members get raped and executed (because that's what lawless paramilitaries do) on the nightly news?
But it won't be their family members, in most cases. It will be some despicable "cultural Marxists" or even more abstract "terrorists". And the rapes? Fake news.