Altium Polygon Pour Order Issues
I appreciate and thank all that provided the above comments to my issue and perhaps some of the suggested solutions may work with something similar but I determined the cause of my problem.

I discovered that it actually dealt with the actual pouring of the copper. Once the original larger copper polygon was poured, trying to overlay a smaller copper polygon with copper already present, it just did not pour as there was not any empty space for the new smaller polygon to pour. When I shelved the larger polygon, poured the smaller polygon, and then subsequently repoured the larger polygon, both polygons behaved as they should have. I was too used to EAGLE auto repouring all polygons.

I accidentally discovered this because for whatever reason, I chose to shelve the larger polygon so I could line up the smaller one where I needed it to be and then unshelved the larger one and it poured around the smaller one. I think the pour order will be only important if you chose to shelve multiple polygon pours and then just restore them all with the single click of restore all or repour all.