You don't usually Ambush as Assassination. Mutilate and Ambush are very close in terms of Damage per Energy, but Mutilate can proc Blindside, so in a PvE scenario that outweighs using Ambush. There's no reason to Vanish that early either, since that will cut your autoattacks. Assassination is all about sustained damage, automatic attacks and poison procs provide the majority of your overall DPS in most situations. You don't necessarily want to pop CDs that early either, but that depends largely on the encounter and your group's tactics.
In PvE you aren't likely to kill anything in the 1st few seconds, so don't worry about initial burst. Your first goal is to get your rotation going smoothly. After that you look for opportunities to get the CDs and procs lined up. It's not about using everything you got as fast as you can, but about using the right tools at the right time.
So, here's a much better, smoother and less busy way to open as Assassination in a Raid environment.
Open with Mutilate -> put up Rupture. If Blindside procs use Dispatch and then SnD. If not, Mutilate to SnD.
In general, Muti above 35%, Dispatch under 35% health. It's worth noting, that Blindside makes Dispatch free, so during the proc you can Dispatch while pooling Energy. You don't have to Dispatch the second Blindside procs, btw, as the buff lasts for a fairly long time. Learn to pool Energy and time things to get the most out of Assassination's potential.
After you have both Rupture and SnD rolling, you will want to get a 5CP Rupture going, but try avoiding clipping it too early, if you can do that without Energy capping. (If you have Anticipation things are likely to be quite a lot easier.) Envenom to Refresh SnD with whatever CPs you have. At this point you will have both Rupture and SnD running for a long duration. This is when you start looking at CD usage. You'll also want to maximize your Envenom uptime without clipping the buff, if at all possible. However, better to clip Envenom than cap on Energy.
Vanish to Mutilate is a good way to eek out a bit more damage, especially with Shadow Focus. With Anticipation I often find it worth using Muti/Dispatch even at 5CPs, if I'm about to use a Finisher after, since Relentless Strikes will refund you with Energy, meaning you might Energy cap. The difference in overall damage is likely to be negligible, but if you're aiming to maximize performance, it's something extra you can do. Also, if talented for Elusiveness, Feint can be used as a small Energy dump as well, and your Healers will appreciate using it. With the current tier set bonuses cutting the cost of Abilities during Shadow Blades, I often try to spend a bit of my Energy before using it to - yet again - avoid capping on Energy.
You'll want to stack CDs together to maximize DPS, and when possible, stack them on weapon enchant and trinket procs to get the most out of things.
As you can see, a big part of Rogue and Assassination PvE is about proper resource management. This spec is about rhythm, think of it a bit like a dance. It's not about how much you do, but about timing things in the best ways.