First off, please forgive me if I don't get the terminology correct. I am decent at home repair but have no real training other than trial and error.

I'm trying to re-do my kids' bathroom, which has not been updated since the house was built. I removed the old tile floor and mortar bed and found that the toilet had leaked in the past. The floor was rotten in some places, though not totally gone. It also seemed a little too flexible in other areas-- certainly not as strong as I expected. Since I figured it would be another thirty years before the subfloor saw the light of day again (after I tile it), I decided to replace the subfloor. I have most of it up now and that went fine. My question is this:

I have a PVC soil pipe with a closet flange assembly that appears to be glued onto the pipe. Just in case I am not using the right terminology, let me describe it:

There is the PVC pipe that allows waste to leave. At the top of the pipe coming up towards the floor, there is a PVC flared piece that rises up to meet the toilet. There is a red flange that sits on this flared piece. The flange is smaller than the flare so when you pull the flange, it would pull upward the entire assembly.

The pipe itself and the piece that flares out to meet the toilet appear to be in fine shape and do not seem to need replacing. However, the red metal flange is showing signs of corrosion and wear to the point that I am not comfortable continuing to use it. However, since the flared piece of pvc is wider than that flange, I cannot simply remove it (i.e. it gets stuck on the flared part of the pipe and can only go so far).

How do I replace the red flange without cutting the pipe and putting in a new one? What is the proper procedure to lay the subflooring with a hole so that I can get the flared piece and the flange above it (so that I can eventually have the flange screwed in and flush with the new tile floor? Any advice from the experts is greatly appreciated!