Sharing a private key is like sharing the combination of a safe, both people will be able to take out the valuable items in it.
Exactly, by sharing your private key you also share the location of the safe (address) and the list of valuables inside ( anybody can check the BTC stored within address).
The other guy can just wait till there is more BTC stored before moving them.
-- DO NOT SHARE YOUR PRIVATE KEY EVER --
What if 2 people have the private key. What happens then?
The public key you can share that is ok. The private one you shouldn't unless you trust that person with your wallet and the bitcoins contained within. It is a good idea to back up your private key in several places as well as keep a paper copy in your safe for example. A ledger would be best if you feel its worth the buy. Remember to keep your key safe. You sre in co trol of the safest and security of your own wallet. You are the bank !
I don't think storing private key in several places is the best way ( more places stored = higher chance somebody finds them ) so this is quite counterproductive.
Better to choose one or two really safe spots which you will be aware of after years (there is lot of users who dig the private keys so deep they was not able to recover them = BTC lost)
also I would recommend to avoid marking the backup as bitcoin wallet or similar ( so the random finder can't be sure what this 'string' can be used for )