Here's some tips for when the action actually heats up at the palace:
Soris, your cousin and party member, has a sword and shield spec, so be sure to equip him with them to take advantage of his enemy-crippling Shield Bash. (I learned that bit late and found it made a huge difference.)
Give Soris AI command to heal himself when necessary. He can be pretty vulnerable if not careful.
I also recommend switching to crossbow for long-range enemies instead of charging them, you have 2 to often his one. hehe But that's up to you.
Dogs (Marabis) will actually be tougher than people so concentrate on those first if possible. Though you may want to divvy up the enemies it may be best to gang up on one enemy at a time to whittle them down faster.
I realized too late that I may be able to steal keys from people and guards. So if you're a rogue you may want to try which could unlock the "key required" metal doors.
Every time you see the game auto save for you, prepare for a big battle. The last encounter before Vaughan will be his bodyguard who will rush you from the end of the hallway with an ice spell leading his charge. He will yell so you should be able to dodge him. This will be I think the third big encounter so just stay alert.
Vaughan himself is easy enough. I didn't take his money so don't know if you can avoid a fight. But the fight itself wasn't too hard. Soris will take on Vaughan's lackeys. You should focus on Vaughan as he definitely has a hard on for you. As a rogue, the talent Dirty Fighting will definitely come in handy in stunning him for a few seconds at a time. Below the Belt will also help knock him back a bit.
Once you finish the fight go back to the Alienage and agree to be part of Duncan's Grey Wardens. Leave with Duncan and you've finished your origin. Congratulations!