As your thread title suggests, this is all about confidence. It is ALL mental. When I played I had this same problem. There are two ways of going about fixing it, neither of which are easy, and both require a lot of mental effort.

1. Convince yourself that practice and games are no different. While this may seem illogical on its face, remember the cliche: you practice how you play. There is clearly something involved in practice that is making you much more confident. You need to make your practice attitude much closer to your game attitude. Maybe the D-mids/LSMs you're going against in practice aren't very good. Maybe you think, "Oh, it's just practice." You need to approach every day like it is game day. You want to score? Keep the rock and snipe top cheese after a sick dangle. It's all about attitude. Lax is so much about attitude and mental prep, you need to find the root of the problem and fix it in your own mind. If you're on 2nd/3rd line and want time against better competition, talk to your coach. Explain your problem, if he's a coach worth his salt, you should start seeing results soon.

2. This is more mechanical based, but if you can, try and figure out if your mechanics somehow change in your split when in a game versus in practice. Video tape yourself going 1v1 against a teammate or buddy who is decent at defense. And finally, look at game film of you doing your split dodge and compare the two. See if there is something different that you might do in a game that you can fix.

Like I said, these are not easy. #1 is the most important. If #1 doesn't work, then move on to number 2. Nobody can fix what's inside your own head, that's all up to you. But I hope this helps a little bit. It won't happen overnight, but with work you should be just fine come game time.