it's part of showmanship. giving ace, calf calm etc blurs the difference but doesn't help you solve the problem.
all along, have people walk up to the off side of the calf, scratch on it, feed it, whatever.
for some reason, people don't understand that prey animals have difficulty focusing on things on both sides of their body.
a calf that moves away easier from one side than the other is merely telling you which side to work on.
spend more time where the problem is rather than the opposite which actually reinforces the calf's position which is to continually rationalize that you need to be where he is more comfortable.
you have basically discovered one of the key sorting components of showmanship and it should be there. the situation is allowing you to see what needs to be worked on earlier, but doesn't help you in the short term unless you work on the other side calmly and quickly.
http://www.youtube.com/watch?v=jB7vIYhhUlM&feature=related
at 1:10 of this video, look at the hind leg move BACK instead of in front and across which means the horse is still going and engaging going forward. when the animal moves their back leg back, they are disengaging. when you can do and understand this (from either side), you will be more comfortable with your animal. you should be able to do this with any animal as they do this to each other and understand it whether it's a predator or prey, or two equal animals enforcing dominance.
notice how he holds the reins, he lays them on his fingers, he doesn't have a death grip. pretend you lead rope is barb wire to help you make your signals more clear. this will require you to move your feet rather than act like a pole and you will start looking for yielding to your cues. each side will be different in their response and for a variety of reasons, the right side of animals are stiffer and need more work, yet we do most of the work on the left side which needs a lot less work. again, the right side is where the judge will be, as well as your competitors, yet again, people try and make the left side perfect hoping the right side will get better.
these are universal principles and pretty easy to do once you understand them.