I think that is too much afternoon sun for them. It will stress them and sometimes stress leads to problems (like lacebugs on asian azaleas). They will need more water (not a good thing a drought), and the foliage will not be as attractive.

Morning sun is best, up until 2 pm in the summertime if you have to.

Azaleas tend to have wide shallow roots so dig accordingly. Have the new hole already dug and ready (I like to use a little soil conditioner). Plant them a bit "high" so that they have good drainage. Mulch well and water in absence of rain.

How large are your Natives? If they are quite large, 6+ ft. and have been growing in their present location for several years, be prepared for a very long lateral tap root that must be extracted undamaged, if possible. It will usually be as long as the plant is tall and may be intertwined with other shrub and tree roots and can zig-zag many directions!
Replant the roots at the same depth as they are now growing, if they will be in similar type soil and apply a thick layer of mulch over the root zone. Keep the soil moist, but not soggy for at least a year after replanting.
I would wait until after frost and defoliation, before moving them. Water requirements will be much less, as you will not have foliage to keep turgid. You can move them bare root, if that would be easier. But don't allow the roots to become too dry during the move. Avoid pruning, if possible, as next years flower buds have already been formed then.
My Flame Azaleas (R. calendulaceum) that are in mostly shade, do not bloom well, if at all, but the Piedmont or Oconee Azaleas (R. flammeum) bloom very well, in similar locations.
I have several species that receive morning sun and several others that are in sun for part of the afternoon. Once established, there isn't much difference in moisture requirements between them and the foliage fares pretty well in each location. (All are magnets for the Black Vine Weevil, Ortiorhynchus sulcatus, a European introducion, that has few natural enemies and is difficult to control)!
By the end of summer, the foliage is pretty well tattered from the adults feeding on it.
I would recommend a location with some shade in early afternoon (1-4PM) for best results and less watering effort!
Rb

Thanks for the advice. The 2 Alabama and the 2 Flame are about a leggy 5ft. They have only been in where they are for 1 1/2 yrs. I thought that much sun was not going to work. I found another spot I think thats more dappled sun with just a little direct sun.I just dont have any place thats the perfect morning sun afternoon shade. Hopefully that will work. I'll wait till about Dec and see how it goes...thanks