Red Dead Redemption Undead Nightmare Disk?!?

PS3: i bought red dead redemption and i wanna 100% plat it i was gunna buy the retail disk of undead nightmare but i wanna know will the undead nightmare and the liars and cheaters and legends of killer packs add on to my red dead redemption or do they create a seperate section for trophies cause i wanna 100% platinum red dead redemption and if the disk of undead nightmare creates a seperate place for trophies?!?