I'm a big halo fan so I might be able to help you with this.
With your associated gamertag, (the one you used to purchase the maps) once they're downloaded on your profile, you should be able to use them on your console either online or off. Note: it has to be with the original purchasing gamertag.
It doesn't matter which console you decide to play on with your hard drive. As long as your gamertag is on the hard drive that the maps are on, you should be able to use the maps. Even if you sign into another profile on halo, as long as the original gamertag used to purchase the maps, will be available to play on.
Parental control could be another problem. Halo is an M rated game so you need to make sure that everything is OPEN to allow ALL access to everything. You can change these settings from the Xbox Dashboard under system settings.
I hope I helped you.
