Can you post a savegame, so we can see the situation in a better way?
Anyway, I usually prefer to bypass core worlds entirely by cloaked assault transports. Of course first I create a tachyon-free path to homeworld by suicide runs (fighters, mostly, because they have bonus against tachyon emitters and are faster to rebuild)
The bad news is that homeworlds have planetary tachyon coverage, so forget any sneak approach.
I usually split my attack force in 2 or 3 groups: a single group of bombers and similar; another group of long range ships (frigates, mostly) and another one with short range ships (fighters).
Another thing very useful is the auto-kite feature in CTRL tab. I usually set limit to 5000. This way frigates will retreat away from attackers, giving them longer live. In this case, use attack-move (X + right click): in this way, when no more targets are in range, your ships will return to the assigned place. Otherwise they will be all scattered around, because of auto-kite behavior.
and yet, use scout starship for anti-sniper coverage; use mobile dock for repairing ships; don't underestimate long-range engine-damaging lasers of riot control starship; don't be afraid to conquer any planet close to your ones, easy to defend, in order to gain other knowledge.
