Cannot speak to the rotation.

I'm using Mercurio's two-step, mindless mash away macro.
I don't have a problem with their DPS, but don't have any damage meters on.
And they're killing mobs at this stage, not full honor geared opponents.

I'd have Tremor totems, on round-robin.
I'd glyph one of your Healing Stream totems, for the resists, and have that shaman always drop a Healing Stream.
I'd have a key for everyone to drop a Grounding Totem.
I'd have a key for everyone to drop Earth Elementals and another for Fire Elementals.
I would not include Searing Totem, in the mindlessly mashed macro... as that will remove the Fire Elementals; which means a key for everyone to drop Searing Totems, and to remember to press it often in combat.

If you have any aspirations towards PvE, include a Paladin or Druid on the team.
Why those two? ... Because they're easy to tank with, and have a useful off-spec.
The Pally can heal your team in PvP, or be a full fledged tank for AV/IoC or a tank-flag runner.
The Druid could heal your team, but I'd actually run it as a Boomer and never heal with that toon (use the Shammies); Boomer gets you 8% spell power (Earth & Moon), Solar Beam, Mark of the Wild, etc...

Until you have close to full Honor gear... at least 3/4's, stick to the 40-man BG's.
AV rocks, and IoC (on its weekend) is as good.
On a non-IoC weekend, you'll likely not find a better BG than AV.
You can run Tol Barad as often as possible too.

Priority is:
a) The two-minute trinket.
b) Two pieces of Honor gear, for the 2-piece bonus.
--- If the guantlets extra thing is useful, make them one of the two.
--- The Helm should be the other.
c) Other honor pieces, that have the color sockets needed to activate your Meta Gem in the Helm.

You won't be able to buy weapons, until you've spent a minimum number of points.
Weapons are worth a lot, and you should save Honor so you have enough to immediately buy them at the same point where you've earnt a minimum of xxx honor that season.

Conquest is similar to Honor, with a proportional amount of improvement to the points spent.
So you can upgrade whatever honor piece you want.
Or if you don't have an Honor piece in a given slot, but have Conquest then that's a no brainer.
Conquest weapons require 7800 conquest points, in the current season... same deal as Honor, but much more important.

You get Conquest for wins in the BG Weekend battleground.
And once you have full Honor gear (or close), you can try Arena for Conquest points too.
You can also run your team in 2's or 3's, if that works better than 5's.
Or play each toon solo; I paid someone a hundred gold a win, to partner with my DK's when they were new and the season had already started (they were very undergeared).; that's an option too.