Edit: I had to edit this post because of errors.
I finally managed to get used to tabs having the A-string on top, but I cant seem to remember that they come first in a horizontal chord description. They are the ones furthest away from me when playing, dammit!
I am missing the possibility to cross out text when editing
It seems to me that 0202 has little to do with a D-chord.
Isn't that more like a G6 or Em7?
#Edit, forget that
0202 on a gCEA tuning will give you the notes g, d, e and b.
#Edit, forget that, its a, f#, c and a again
A D7 chord will need d, f#, a and c. Not necessarily in that order.
The only note in common is the d.
#Edit, only chords missing is the d
If you practice a bit you will probably find that barring the second fret and playing the 2223 is not the most difficult chord to play.
#Edit: I mean 3222 og course, I keep looking at the order of string the opposite way of what I am supposed to.
In my opinion it is easier that the normal D chord.
The dreaded E-chord is worse. To begin with I considered substituting it with E7, as E7 in my experince is so much easier than the E chord.
Anyway, if the chord works for your song, I guess you don't need to change that