Okay, hold up.
Firstly, getting Rebel and/or Confed ships has nothing to do with dominating planets. You do need a high combat rating and must be well-liked, but you aren't required to have dominated any planets.
Secondly, if you already have the particle beam you're only one short mission string away from being able to buy Confed ships. I know that opinions differ, but IMO, for raw hitting power and the shields to take a sustained assault, nothing beats the Confed Cruiser.
Thirdly, until you get Reb/Fed capital ships, the Kestrel is the best ship in the game. If you're having trouble with rapiers try upgrading the kestrel with the speed/turning/acceleration upgrades, shield booster/capacitors and some armor plating. The Kestrel should serve you well.
BTW, all of this advice is assuming that you're playing standard EV without any plugs. If you're using plugs, some or all of this advice may be incorrect.
------------------
Jon Potter
Thank you for your cooperation. Good night.