I did some tests and I think I have a clue about what's happening.
First of all, I'm using SkyElite with Just Flight's PA-28R Arrow III. I think this is very interesting. As I told you before, the problem is that the CDI key doesn't switch from NAV1 and NAV2 to GPS. The FPD only shows NAV1 and NAV2.
If I configure the airplane to display GPS: GNS DUAL, then SkyElite works fine.
If I configure the airplane to display GPS: GNS 530, then SkyElite works fine.
…But, in case I configure the airplane to display GPS: GPS 100, then Sky Elite fails and doesn't show the GPS option. So that it seems that the bug is for some kind of lack of communication between both programs when GPS 100 is in use.
I think this is not a serious bug, as I think few people will fly with the GPS 100, an old device (and very ugly, by the way), when you can use a more modern GNS 530. At least I consider the problem solved.