The problem is likely a mix of bad source data and HDR alignment issues.

First, if the sky is blown out in one or more exposures, there is no recoverable detail there. HDR can’t recreate detail from clipped pixels, so tone mapping may turn that area into flat or ugly patches.

Second, Luminance HDR may be correctly detecting that your brightest frame is only about +0.32 EV, not +2 EV. If you force the images to incorrect exposure values, you create inconsistent input, which can produce unnatural tones like the gray sky.

Third, movement between frames—especially tree branches—can cause ghosting or alignment artifacts, and those can show up strongly in the sky area near the branches.

To improve results: use the exposure values the software detects unless you know the metadata is wrong, avoid clipped highlights in the sky when shooting, and enable anti-ghosting if available. If branches or other objects moved between shots, that can also explain the artifacts.