I'm working on trying to play chords and such on a violin as if it were a guitar or another stringed instrument, but I noticed when I play chords (like the G chord), the open D note rings out and is much louder than the other, more dominant notes in the chord. Why is this, and how can I fix it?
Part of the reason might be that you have a poor quality violin. There should be a resonant frequency of the air inside the violin body that is close to the frequency of the open D string, but if it is too close you will get the effect you described, especially if the body of the violin is not very resonant or the body resonant frequency is too high.
See http://hyperphysics.phy-astr.gsu.edu/hbase/music/viores.html for a diagram (and compare with the measured resonance curve for a Strad, http://hyperphysics.phy-astr.gsu.edu/hbase/music/viores.html#c2).
If changing the strings doesn't help, it might be possible to improve the situation by moving the sound post to alter the body resonance, but don't try to do that yourself - get some professional help.
As I've said in the comments, open strings are generally a little louder than they would be if they had fingers on them.
The fact that you say your G string is actually quite than the D string makes me wonder if the strings are the same brand.
Another thing to take into account is string gauge, or how thick or thin they are. Usually, people go with medium thickness. But look at this:
Almost all strings are available in different thickness or gauges, for example Thomastik Dominants, which are available in stark (thick), mittel (medium), and weich (thin). Pirastro Eudoxa, Olive and Kaplan Golden Spiral gut strings come in a variety of gauges indicated by gauge numbers. The majority of string players use the medium gauges. In general a thicker than normal string will require more tension in order to bring it up to pitch. This increase in tension will produce more volume and sometimes a fuller sound but with a slower response. A thinner string requires less tension and will give a faster response, but with less volume and a thinner, slightly more focused sound.
It's possible that the D string is a different gauge than the other ones, although I don't know if it would make that noticeable of a difference.
What are your strings made of? I don't know how much material will affect volume, but the strings are part of different sets, this may be the answer.
Another thing to consider is that the problem may be with the G string, not the D string. Violin strings are supposed to ring out fairly well, but when they're old or dirty they tend to lose some of that quality. Is it only the D string that is louder? And, did you last change all of the strings at the same time?
Hope some of these ideas helped. Happy playing!