The SD's do have a long trigger pull, and it takes work to get it under control. But we're skipping a step here with the OP's problem to talk about mastering the SD trigger... although I'll come back to that in a moment.
The real question is, is the OP getting a scattered group of hits because the gun is not accurate, or because his technique is not giving him practical accuracy, that is, repeatable success in firing the gun well.
Is the OP's SD accurate? Does it group closely and shoot virtually the same place all the time, preferably where aimed, but always hitting the same place in relation to the sight picture? If so, the barrel, lock-up, timing, ammo, etc., are all doing their job to be accurate... but the sights are not aiming where they are supposed to.
In which case, if he is not hitting where he is aiming, but the groups are small, the gun is accurate but not sighted properly. Left/right can be solved by drifting the sights; up/down is harder to fix but can be solved by adding a higher or lower sight post, or, if hitting too low, filing off some of the front sight post.
But, if the OP's pistol is being fired the same way every time, but the grouping is scattered, then the problem is probably the gun. That's what sounds like might be the case here, especially if other folks with the OP are having the same problem with the OP's SD9VE. This is why people use Ransom Rests (which mechanically align the gun and press the trigger) or, if a Ransom Rest is not available, they use a sandbag or other aiming assistance to lessen human variables.
If the problem is the gun, that is, it shoots differently each time even though aimed and triggered consistently, the most likely problem is the lockup of the barrel with the breech face. Sometimes this can be seen visually... The second most likely problem would be a barrel that is flawed in some way - bulged, bent, pitted, or suffering damaged rifling, a nicked crown, a peened barrel hood, etc. The solution is to buy a new barrel (Numrich's is listing new SD9VE barrels for under $75, and there are currently several used SD9VE barrels on Ebay for around $70).
But one test that might be worth conducting before buying a new barrel is to try different types and weights of ammo. Some barrels (and pistol actions in general) work better with different types of ammo. Most people shoot 115 grain 9mm, but 124 grain is widely available and 147 grain can be found, too. Each works the gun a little differently and OPs SD-9VE might favor one over another. Brands can vary too.
An underlying problem with the SD-9 family in working through this is that durn trigger, which makes it harder to control your shooting precisely and the same way each time with this pistol -- compared, say, to an expensive 1911, Sig, CZ-75, etc. So while one is trying to figure out if the problem is the inherent accuracy of the pistol or the ammo or some other problem, it can be hard to isolate the key variables.
