So the dungeons are significantly harder than they used to be back in the day. If you're not running it with a full group it's a huge disadvantage and I'd say your doing great regardless.

Because a lot of fights are now movement heavy with mechanics mobile DPS is favored, which is primarily Beastmastery Hunters. You can still of course pull it off with other classes but your DPS begins to drop unless you weave in some instant casts here and there.

You just need movement keys for your non main group to weave in and out of these, so when you press strafe left only your Resto Sham/Arcane Mage go left while your prot war stays.
For me, I use WASD for main only movement, alt - WSAD for everyone but the main movement, and the arrow keys if I need to move the entire group.
Another nice trick is if the main doesn't have to move much, I'll swap to the healer and have the team follow that character and then dodging is a bit easier by just running around. If the tank needs to adjust, swap over and move and then swap back.
A good example of this type of fight is the last boss in Freehold. The tank doesn't have to do anything but tank, while the rest of the team is dodging artillery strikes, this keeps them clumped together well.