Unfortunately you cannot mirror live streaming of games via the MLB tv app on the iPad 2. It's frustrating, that was one of the main reasons I purchased the iPad 2. I bought the Apple AV adapter, an HDMI cable, and the MLB tv app from the app store, and have an MLB tv premium subscription for the year. On the iPad 2, the game streams beautifully, but when everything is hooked up only the sound goes through my HDTV, not the video. I know this is not a blackout issue because it streams fine on the iPad, and I know it's not a mirroring issue because as soon as you exit the MLBtv app the mirroring works fine (everything you see on the iPad screen you see on the TV.) Netflix streaming works fine too - I hook up the iPad 2 to my TV with the same equipment, same adapter, cable, etc. with no problem.
I have emailed MLBtv support but have not heard back. I don't see any reason why the MLBtv app would block video mirroring, because with the same MLB subscription I was able to hook up my laptop to my TV and watch the game that way so I see no reason why viewing the game on an iPad 2 vs a laptop should be different. Hopefully it is only a technical issue and an update of the MLBtv app would fix it.
So long story short, at the moment you cannot mirror MLBtv games to your HDTV via the iPad 2.