Different from First Prince or not, she was still declaring herself the legal head of state rather than the regent.
Declared all she wants, what held her in power was regiments loyal to her being nearby.
That and the fact that every other S-D heir was off world at that point.
All she had legally was Regency which is why she used the title "First Princess".
Morgan was never a member of the Lyran military,
Since when? He served with the LCAF in the 10th L.Guard & 10th Skye Rangers both after graduating from Nagelring with record scores.
If he'd really opposed her actions, he had other things he could have done: trying to arrest or assassinate her might have been an unrealistic goal but he could have easily done what Adam Steiner eventually did and declared himself and his forces neutral in the conflict. That would have done a lot to weaken her.
What forces did Jackson have loyal directly to him & where were they?
And there was no conflict till after she had been in power for a few months & in that time had already made changes like removing Ardan as Prince's Champion which she also didn't have any legal right to do but if people chose to follow her orders, well, it was more than Jackson choosing to just follow the person sitting on the throne.
Victor was outside the IS when it happened & when he got back he chose not to act right then when he had the power to do so & the full momentum if a grateful IS behind him.