It sounds like to me you just need to spend time practicing the D Chord.

The D Chord is my most natural chord and happened on accident. When I started I would always play the D Chord, with Dsus2 (D with open e string) and Dsus4(D with e string fret 3 with pinkie hold original chord). You can create a lot of easy interesting chord progressions with those 3 alone. You can also pluck through them randomly and discover a lot of easy little riffs. Get the pinkie involved early. If you play Em with index on A (5) and middle on D(4) transitioning to D is easier however you should practice it both ways (middle, ring). you can also do a D7 which is like reverse D fret one on B instead three. The sus stuff works with that one too.

Also whenever you hold the guitar fret the chord you find most challenging it makes the shape stick.

Play the just the D chord and sus2 sus4 for awhile then try Em chord. I bet it will be easier.