If pronation or supination doesn't apply...
Everyone has trouble turning right at first because all the !#$!*& rinks make you skate counter clockwise at the open skates.
But seriously, this doesn't sound like an ankle strength issue. Does your ankle twist when you try to put your skate the right way, or is your skate never getting there in the first place? If it's never getting there, it's you! You aren't shifting your weight onto the oustide edge of the blade. That could be due to your overall body position. It could also be that you don't have confidence in the support your skates give you.
Try turning left and pay attention to how your body is oriented, where your feet are in relation to your torso, how your shoulders are lined up, how much you are leaning, etc. Then try turning right and see what is different about your body positioning.
Most importantly, player skates have a lot of support. When they look like this / \ , it's usually a sign that the skates are too big or too loose and are turning on your foot. You have to fit the skates properly and tie the skates snug. Unless they are Missions, they should be about a size to a size and a half smaller than your shoe size. But that's just a rough estimate. If you aren't familiar with fitting skates you should go to a pro shop with knowledgeable sales people who can help you out.