The original cata dungeons are very tough to multibox. The hour of twilight dungeons are much easier, but not until you're geared.

But you shouldnt have too much trouble running dungeons at your level. My teams leveled alot through dungeons so I could skip the collection quests. Sounds like you just need to work on your macros and keybindings so you're able to move freely and have more control over each toon.

The Naz'Jar Sentinel you speak of has an ability that absorbs healing on you for 10 seconds. Its not any damage just cant be healed during that time. If I remember right he also drops green stuff on the ground your toons have to move out of.