Can I have a downloaded game (Minecraft) on two PS3's at once?

I just bought a second PS3 for the house so the kids can play minecraft in a different room. I can't seem to keep the full game version on both machines. Whenever I download the full version on one machine, the other machine goes back to the trial version. Since I paid for the game and own both machines, it seems like I should be able to have the full game on both machines. Is this possible?

Note: I had a terrible time trying to set this up to this point, creating separate profiles for me and my daughter and even creating a new PSN ID for my daughter. I have had two common errors about not being able to sign in with another users ID and also only being able to have 2 PS3s activated at once (which drives me crazy because I only have two machine so why do I need to deactivate anything at all?)

On ps3 1, sign in to your psn. Purchase minecraft, you don't have to download it if you don't want to. Next, sign out of ps3 1, then on ps3 2, create a *user* account for yourself, and a *user* account for your kids. Ok, now open the user account you made for yourself, and go to create psn account. Go to "log in to existing account" and sign in to *your* psn account. Once in your account, go to "account management>downloads" find minecraft and download it.

Ok once that's done, sign out of your psn account AND your *user* account. Once out of both, scroll uo and create a new user. This will be your kids user account. Once in, create your kids psn account, or select log in to existing account as you did with your user account. And that's it, minecraft should be on that ps3, and available for all users.

NOTE the psn account that purchased minecraft must be a master account, othere is other users on that system will not be able to access the content.

Did you delete your profile right after you downloaded the game to the second console? If so then you need to sign in again and download the game after that don't delete your profile on the second console(you can sign out but don't delete the profile) and you should be able to play on both consoles.

Another reason could be that if you bought the game digitally and it contained a trial version and it came with 2 download files(one being the demo and the other being a small size download usually named full unlock or unlock key) download both on the second console.

Try these options and see if they work.