If the skylight is two piece, would I be able to unscrew the interior piece and replace it with the tinted one?
Probably not, the tinted one is probably the "hail shield" portion of it that goes on the exterior.
We're getting all the windows tinted but they can't do anything to the skylight and I do not want to put one of those foil type things over it. So I'm just trying to figure something out while it's not so hot.
After I read your original post and replied I realized that our shower skylight is actually tinted. The tint really isn't that impressive, it looks good and all but when you factor in that it's pointed directly "up" you realize that there really is a lot of exposure to the sun unlike a window that will only be exposed when the sun is on that side of the house. If you're looking for additional insulation you might want to consider using Mylar like you see in some RV windows, it's kind of like reflective bubble wrap. The down side is that it will completely block all light from coming in but it will also pretty much eliminate the heat problem you're experiencing. Then when the temperatures drop all you have to do is drop the inside skylight and remove it.
Personally, I'd stay away from replacing that clear hail shield simply because you'd have to remove the sealant that protects your roof around it. Re-applying is not too difficult but I just don't think that a tinted hail shield is really going to net you that much improvement. Here again, we all have our own tastes and requirements on these things.