First welcome to the forum. Also, your Dolphin was made buy National RV, out of Perris Ca., who went of of business in 2008. (No Problem). I would also like to point out that IRV2 has a forum just for National Owners: National RV Owner's Forum - iRV2 Forums
(A moderator may move your post there)
I just finished putting in AllureⓇ vinyl flooring (myself) in my '99 34ft Dolphin with a 12x3 ft slide. There is no need to tilt the slide out. Just extend the slide all the way out. The carpet will be stapled just an inch under the slide. I took all the carpet out and left about 3 inches hanging out from under the slide. Then I just ripped it out. There will be pieces left as well as some staples. Then with a good pair of pliers, block of wood and a crowbar, you can raise the slide face up enough to remove remaining carpet pieces and staples as you move along the edge.
Once all carpet is removed from the MH, there will be between 10 and 20 bazillion staples to pull up, a real PITA.
In several places, you will see large phillips screws in the flooring going through washers. These screw into the frame. However, no matter what I tried, I could not get them level or below the flooring surface. So I removed the washers and did it that way.
Now comes the real important stuff. The slide face will have 5 solid nylon puck/sliders. 2 on the couch side and 3 on the dinette side. These work fine over carpet. But they will scratch the hell out of a vinyl floor. They can also scratch up a very hard surface laminate. Part of this problem is the weight these 5 sliders have to carry. Mine were only 3 inches long and maybe 3/8 wide. Figuring they are carrying close to 1000lbs, that's a lot of weight on a very small amount of square inches. I tried 3 ideas before I got it right.
The last one was to eliminate the nylon sliders. I made six blocks of wood out of 6x1x1/4 inch oak. Glued carpet to them, then glued those along the leading edge of the slide. We've had the slide in/out at least 10 times now with no scratches. One more tip, make sure the flooring extends beyond the sliders when the slide is all the way out. If you don't, the carpet can be pulled off as it makes it's way up onto the flooring.
My Dolphin is 2 years older and there may be some slight differences, but I doubt very much.