Frankly i think Prince is the hardest boss in UK. So much spell damage so fast can be tough for tanks (except maybe a DK).

The adds are skellys so poly wont work. Shackle would be a waste of time. You can holy wrath with the pally to get agro on them and do some damage. Just pop AOE a couple times on the mages and you should be fine with the adds. If the timing is correct it will kill the tomb as well. Just watch your mana when spamming arcane explosion.

You will definately need a dedicated healer for instances. The holy priest is the easiest to box, just macro a circle of healing / prayer of healing targeted on the preist to a key so you can quickly get your followers healthy with a simple key press.

Prince is a pain with the shadowbolt spam, make sure you have shadow protection on. If your tank can keep agro and you have some TBC shadow resist gear it makes the fight easier. Matter of fact shadow resist gear is just nice in UK. Too bad blizzard doesnt really have any end game resist gear anymore.

Pop mirror image before the skellys come so they focus on Prince.

Good luck!