I think you will find that your alternator has a fault or u r just simply pulling 2 much power.
I would like to reconmend something that no1 else has. Capacitors, they can be a little expensive but the volume and deepness of your bass will increase fairly noticably, if u listen to hip hop music (large low long bass lines) i would say capacitors r a must. Capacitors will also stop the "dimming" problem if u dont want 2 upgraded 2 a higher amp alternator, infact they would probably do a better job as well as making your system sound beefer.
Also if u r running two 12's why buy 6x9's? there is no point running a larger cone, u have plenty of bass, unless u plan 2 filter them 4 midbass instead. i would say a set of 3-way splits would be better use of that money or use a 6" ,4" and a tweeter for a mock up 3-way speaker setup.
Any decent stereo shop will be able to help u with this, on that note, Tonkins Car Audio does very good work- having worked there myself I no wot happens behind doors