Hi!

This chord was quite tough for me as well. I'm still slow in some changes, but in the usual progression with Em, G and C it comes quite well at this point.

The moment of revelation to me was the direction of fingers. On top of having them straitht, with space with the bottom of the neck, etc, I also realized to keep them very diagonal with tips oriented towards the body of the guitar. The thing is that normally you come "frontally" with your fingers, but with D is not effective, as most likely at least one of the 3 is not gonna sound, in my case was index, as it was remaining too far from the metal of the fret. When I place my finger in diagonal, all fingers can slide easier towards the metal, and voila it rings much better. Watch out also middle finger, as in my case it tends to slip beyond it fret. Have a look at videos and pay attention to this, you will see what I mean by diagonal. Then compare to yours and check if you are oriented this way. At least this made the trick for me. Good luck!