Does BIP44 key derivation path protects private keys derived within same account?
Bip44 doesn't protect anything, if the user has master root key, they could get access to all the other accounts private keys.

Your path is wrong, it should be like that:

m / purpose' / coin_type' / account' / change / address_index

What you should do is generating child master private key for the following path:

m/44'/0'/1'/

Now the user has access only to account number "1" and should generate addresses using that child master private key and the following path:

m/changeAddress/addressIndex