Basically, Solomani Security Peacekeepers handle most internal security issues.
It takes a while to mobilize the heavy units of the Confederation Army, so they're usually not committed unless the situation is dire, which may be overdramatic, but if the situation warrants it; if a Paratroop Division drops in, it usually is meant as deterrence and/or tripwire.
Dirtside, Confederation Marines will act as shock troops to take out strategic or operationally vital nexus, with the expectation they will be relieved by other Confederation forces.
Home Guard units are subject to being Confederalized, in most cases to coordinate training with the Confederation Army and Navy, occasionally, reluctantly, for expeditionary combat missions.
The Confederation is reluctant to directly employ mercenaries, and would prefer to outsource that to allied third parties, mostly as plausible deniability, if things go tits up, or awkward events happen.
The CAVALRY was originally established to act as auxiliary troops for Navy ground missions, which they didn't want to commit Marine units for; currently, acts to fill in the gaps in the Confederation military force structure(s).