I see from the preview that others have already said most of this, but since i've wasted all those keypresses I might as well post it anyway!

When this happen what is the best chance?

Drop the tank and play with the others?
Try to get aggro with the tank?
It depends on the encounter

Some random target events are all about just being able to survive, in which case there's nothing you can do except heal whoever's under fire. You should be able to do that while still "playing" your tank, even if it means resorting to some sort of AoE heal.

Sometimes you just need to stop DPS for a while and taunt.

Sometimes there's a specific thing you need to do (like get the hell away), in which case you may well have to switch to that character. To be honest, I never do though. Between global "move" commands (forward, back, strafe) and follow I can usually get away.

When you have trouble with specific encounters, it's worth posting here to see if anybody can help. Personally, I had a terrible time multiboxing TBC instances so I can't offer much useful advice on them, but I know others fared far better.

For the first boss in UK, I keep my entire team on follow until I engage. They stand about a foot behind me, because there's no reason for them to be any distance away in that encounter anyway.

My tank of choice these days is a Bear (yay.... aoe tanking with no cooldown!), and I have swipe in my tanking macro so I tank all the adds.

I know nothing about warrior tanking, but I'm led to believe that all tank classes now have some sort of AoE attack, so it should be entirely possible for your warrior to tank the whole lot.

Above all, though, don't be disheartened by the difficulty of Northrend instances by your experiences in Outland - Northrend instances are just nowhere near as tricky.

And don't forget there's a tactics forum here - I cracked some seemingly impossible fights thanks to some of the guys around here!