The accuracy of any handgun depends on a number of factors and the accuracy of a 1911A1 pattern gun adds in a few more.
There are three basics common to all, the gun, the ammo, and the shooter.
Find a shooter, of demonstrated accuracy, and have them shoot your gun and ammo.
If the results are not drastically different, then the issue is most likely not you.
Get some different ammo for your gun and see if the accuracy changes enough to be significant. Try as many different kinds as your budget allows.
If possible, have someone else shoot the ammo you are using (now) in their gun and see if the results are the same, close, or much different.
Each one of these steps helps pin down which is the major factor in your issue. IF you're thinking about a replacement barrel for more accuracy, its best to determine if the gun is the problem, or not.
IF its not you, and its not the ammo, then its the gun, but the gun is a whole raft of things, and it includes how those things work together.
For example, if your barrel is accurate, but the gun doesn't reposition all its parts precisely the same way, every shot, its not going to be as accurate as it could be. And, the opposite is also true.
However it is not as acurrate as would like.
This is a big question that needs to be answered up front, or you're just going to waste money and time.
How accurate do you think it ought to be?? Do some research and see the average of other guns. Everybody wants "match gun accuracy" and "combat reliability" and that's a tough thing to get both of.
If your expectations simply aren't realistic, you aren't going to get them easily, or possibly at all.
Commander size guns aren't generally made to be match gun accurate, even if they have all the bells and whistles to make people think they ought to be.
People will talk a lot about group size at X range, what is it you're looking for and not getting??
I've got a Colt that will do 2.5" groups at 25yds, from MY hands. That might sound like it could be better, but it's one ragged hole, and I can't do better, and don't expect better than that.
What are your standards??