In terms of privacy, I mean things like a room that is seldomly intruded and stuff like that, where you could easily hide something.
Those two weeks, are they without removing the cage at all? Wearing it to school and such? It is generally recommended to take chastity cages off on a regular basis to give both your body and your cage a thorough cleaning.
In that case, one good option might be time locking. Either using something like a kSafe (https://www.thekitchensafe.com/), or by using a combination lock in combination with a chastity keyholding app. In the latter case, render your key inaccessible using a combination lock (e.g. by putting the key into a combination lockbox, or by improvising a sleeve around the key and preventing its removal with a combination padlock), and use the keyholding app to make sure you only get the combination once the timer runs out. Typically, this is done by changing the combination to some random number without looking at it, taking a good photo (which is admittedly hard to check without looking at the combination, so you might need to give it a quick glance and hope you forget it soon), locking that photo behind the app and then changing the number again once the lock is shut (again, without looking until the opening combination is no longer visible). Using a time-lock safe like the kSafe skips that step, but provides up-front expense. You will probably need to trust electronics either way.
A more low-tech option is to put the key into a cup of water and freeze it, but good luck explaining to your mom and sister why there is a cup with a key inside in the freezer.
The other key should serve as an emergency key. To not be tempted to use it, one solution would be to get a small non-reusable piggy bank, toss your keys in there, and the bank into your bag.