Howdy
The part in question is called the cylinder bushing.
It has one main purpose, to deflect powder fouling blasted out of the barrel/cylinder gap away from the cylinder pin. Not much of a big deal with Smokeless but very important when shooting rounds loaded with Black Powder.
This photo is of the cylinder bushing and barrel/cylinder gap on a Stainless Ruger Vaquero. The only reason I am showing the Ruger is because the photo illustrates the principle very well. The concept is the same with any revolver following the basic design of the Colt Single Action Army.
In the photo, the barrel extension is visible extending to the front face of the cylinder. The cylinder bushing is just below. It protrudes from the front face of the cylinder. Fouling blasted out of the barrel cylinder gap will be blasted out pretty much in a plane from the gap between the front face of the cylinder and the rear of the barrel. The bushing extends forward of that plane and blocks fouling from being deposited on the cylinder pin below. The horizontal separation of the B/C gap and the front of the bushing is what does it. If Black Powder fouling is deposited directly onto the cylinder pin, it will work its way down the pin and cause binding between the cylinder and the pin. That's why the bushing is there, it is a relic of the Black Powder era to prevent binding by deflecting fouling away from the cylinder pin.
The next photo is of the removable bushings from an Uberti Cattleman on the left and a 2nd Gen Colt on the right. The scalloped groove that goes around the front of the bushing may have some effect in deflection powder fouling, but really it is just the extended shape and the horizontal separation it creates that does the job.
Your cylinder pin is designed to be removed. If Uberti told you otherwise, they are full of hooey. It is supposed to be a light slip fit. There should be no interference. If it only comes out partway, then something is binding it in place. Perhaps rust, perhaps scoring on the bushing or the inside surface of the cylinder. But it is supposed to be removable, that is part of the design, going back to 1873 and the first SAA. Cimarrons are made by Uberti, the design is the same on all of them. The cylinder bushing is designed to be easily removed.
There are a couple of theories behind this. One is that a separate bushing will allow the gun to fire Black Powder more easily without the bushing binding. This too is a lot of hooey, I can shoot Black Powder out of a Ruger with its non separate bushing all day long. I also have a Colt that has the bushing so frozen in place that I gave up removing it long ago. In either case, binding is not a problem once the gun has been properly lubricated for Black Powder and the bullets have enough BP compatible lube on them.
The other reason quoted for the removable bushing is that it is an easily replaceable part. Replacing a worn bushing is easier than replacing a worn cylinder. This explanation does hold some water. Early 3rd Gen Colts did not have a removable bushing, the bushing was a separate part, pressed into the cylinder at the factory. It was not removable. However Colt got so much guff over the pressed in bushing, that current 3rd Gen Colts do have a removable bushing.
If you can't get the bushing out, it is no big deal, as I said my Rugers with their built in bushing shoot BP just fine, so does my Colt with the frozen bushing.
However if you want to remove the bushing, and have access to a lathe, you can make up a tool like this to remove it. It is made of brass so as not to mar the steel. The tool is 3" long, the narrow part is .75 long. The smaller diameter is .250 or just a shade under. The large diameter is .330. To use the tool, insert it into the bushing from the rear. The shoulder of the larger diameter will just fit inside the ratchet teeth. Use a light hammer and gently tap the tool to drive out the bushing. If it is stubborn, apply some good penetrating fluid like Kroil and allow it to sit overnight. Once you get the bushing out, inspect it for rust, pitting, or scoring. Gently smooth it on your lathe or in a drill press chuck with some fine sandpaper. Do not overdo it. It should be a nice slip fit, it should not wobble.
Do use Ballistol it is the BP shooter's best friend. After cleaning the gun with your favorite water based BP cleaning solution, apply a little bit of straight Ballistol onto the inside and outside bearing surfaces of the bushing, then slip it in place.
P.S. Single Action Army is a registered trademark of the Colt Company. Other companies make replicas and clones, only Colt makes the SAA. Colt is very aggressive about policing their trademarks and other companies know Colt will sue their pants off if they call it a SAA.