the OP also needs to keep in mind that even in a situation where the HAF would have been separated from the SLDF, Stephan Amaris had a humongous influence on the Child First Lord (who granted was what, 19 at the time of the coup). Kerensky HAD to obey the orders of his commander in chief, as would the Royal Command. there was no bureaucratic method to ensure that the Hegemony was safe from an idiot Director General.
Amaris said devote all of the SLDF to the Periphery Uprisings, Cameron followed the Fat Mans advice cause there is no way Uncle Stephan would stab him in the back. (instead he shot him in the face...)
Richard Cameron came of age in 2762 (at the age of 18) and was 22 at the time of the Coup.
Amaris left Terra in July 2764 (although he'd have remained in contact with Cameron via HPG and by the numerous officials he'd suborned in the Hegemony and Star League government), having made the pact to reinforce the Hegemony with RWA soldiers if needed.
The Periphery Uprising began in April 2765 and in July 2765
Kerensky made the decision to pull two thirds of First Army (the Hegemony's garrison) to replace units pulled out of the garrisons in the Member States.
Kerensky also proposed hiring AFFS and LCAF units to fill out the Hegemony garrisons. Which must have gone down well with the Coordinator, Captain-General and Chancellor. Also, these AFFS and LCAF units would be essentially swapping places with some of the SDLF 1st Army units, indicating Kerensky trusted the Suns and Commonwealth enough to let their troops into the Hegemony but not enough to leave them without SLDF garrisons. It's not the most politically astute proposal to make.
Cameron then announced that per the existing treaty he'd be bringing in RWA troops instead. This was
after Kerensky had decided to weaken the 1st Army.
Kerensky wasn't keen, particularly since the SLDF had been ordered out of the RWR by Cameron in 2755 (which Kerensky didn't
have to do since Richard was only 11 so his authority was more moral than actual, but the general decided to obey anyway) and there were no reciprocal SLDF garrisons in the RWR.
Amaris had reasonable credibility: he was generally considered a bad influence on Richard on a personal level and not to be terribly bright but overall his loyalty was not considered in doubt: he was highly influential at court and his soldiers had reportedly beaten off the local separatists (battle of Gotterdamerung) unlike the other three Territory states that had had massive 'defections' to the Uprising. Even the
SLDF had defectors whereas the RWA appeared to have proven its loyalty by not doing this.
Kerensky would have had to recant his existing commitment to move troops out of the Hegemony to stop this, something that would have had significant political consequences particularly since his reasons would be distrust of someone who wasn't considered a threat on any level except as a bad advisor - not a malicious one.