Yeah, I had the starbase idea too, but the AI quickly countered by simply staying away from them. Most irritating.
First, get some fighters (use carriers, upgrade your starbase, build hangers, whatever is most convenient). Set the fighters to "hold ground" stance and position them around the starbase. Build a few flak frigates and do the same. This should render the starbase impervious to most forces of strike craft. Now upgrade the starbase with "auxiliary government". This means control of the planet cannot be lost even if it's reduced to 0 HP through bombardment. This forces the enemy to attack the starbase if they want the planet.
In terms of splitting the fleets, what would you recommend in the smaller sub-groups?
A Sova Carrier with a few gardas, hoshikos, and javelis is a superb force. The Sova can field bombers or fighters and if it reaches level 6 you can use its ultimate ability to quickly swap between fighters and bombers on the fly depending on what enemy unit types you're facing. Combined with its combat abilities, the Sova can counter virtually any combat units, and the simple forces of gardas, hoshikos, and javelis makes a balanced escourt. If you're facing primarily heavy cruisers, then go with light carriers equipped with bombers. Either hide under the protection of a starbase or else linger on the edge of the gravity well so you can jump out if the enemy gets too close.
2. Is an asteroid belt so I can't plaster the area with defense.
Sure you can. It just means you need to put some frigates on support duty. Use hoshikos instead of repair platforms, a few carriers for strike craft, and maybe supplement its firepower with a few Javelis LRM's. If you really want to play hard-ball, station an Akkan battlecruiser next to the starbase with targeting uplink. Asteroid belts give all units a chance to miss, but targeting uplink will negate most of that, plus it will grant your units an attack range bonus (always nice). You should be able to hold an asteroid belt against all but the most dedicated attacks.
I am suffering horrible losses in this system to keep the enemy fleets away from my core worlds. Any ideas?
If you're doing a lot of fighting in asteroid belts, bring in the Akkan and use targeting uplink. If you can level it up, armistice is a real game-winner. One of my favourite armistice antics is to rig a starbase to explode. I then maneuver my Akkan so that when I activate armistice (hoover your cursor over the icon for a preview of its radius) only my own fleet is affected, and the starbase and enemy fleet are not. I think activate armistice, then blow the starbase. Armistice technically makes the affected units invulnerable, so they survive the blast unharmed while the enemy fleet is torched.