Once you're relaxed and you're allowing the arm to take your hand back and forth between positions, it's time to refine the shift by adding more grace in your finger movement. Picture this:

You are standing with your feet together. You are about to take a step to the left. Do your legs stay totally straight before you take the step and while you are stepping? Of course not! Before you step left, your knees bend just a little, and you can even push off to the left a little, using your right leg as a little springboard to get you to the left with less effort.

The same thing happens with your fingers. Set yourself up on a finger. This finger will be the springboard that gets you to your next position, wherever it is on the violin. Just before the shift, let the finger bend a little bit, just like your knee would, preparing for the shift. Then, bounce off the finger to start your shift, and let your arm carry your hand the rest of the way. Your shifts, when done with this technique, will suddenly be more graceful, fluid, take less effort, and will land with greater accuracy.

Sometimes it's helpful to picture your fingers as legs, especially after practicing with your legs first, pushing off one foot to get to the next foot.

The accuracy and tone of double stops always improve for me when I concentrate on beautiful motion between each double stop. The technique for doing this involves using the current fingers to bounce you to the next fingers. It's essentially the same technique as I use for finger preparation when shifting. If you can successfully do it with one finger when you're shifting, try using that same finger resiliency when playing double stops. You will immediately notice a huge difference.