If you explain your application in more detail, I might find that I'm off base here, but for now I'll make some assumptions about your use case and threat model.
My understanding is that you have some sensitive information that you want to synchronize between a mobile device with intermittent connectivity and some remote service. The service is only accessible to authenticated users, and users must authenticate themselves to the mobile device to access its copy of the information, even if it is offline.
If you want strong security, encrypt the mobile device's copy using password-based encryption.
You could use the same password used to authenticate to the service, but in general, I'd avoid reusing the same key for different purposes. A better approach would be to have a master encryption password for the mobile device, which encrypts the mobile database as well as the "password" used to authenticate the user to the synchronization service. Note that the service authentication password could actually be a private key for SSL client-cert authentication, or a character-based password.
You'll have to evaluate the risk of having just one password, but in many cases, I think the convenience this offers the user, combined with the safety provided by one strong master password as opposed to two weak-but-easily-remembered passwords is a good balance.
Note that this approach will allow user whose service access has been revoked to continue to access their local copy, but without any new updates. You could include some notion of a time limit to be enforced by the mobile software, but a determined attacker could circumvent this.
If you just need toy security, your suggestion of storing the correct hash on the mobile device is adequate, and it really doesn't matter whether you hash the real password or an alternate, because if you use the right hash, it should take them a few billion years to find a password collision that would allow them to access the remote service.
However, assuming an attacker can see the password hash, what's stopping them from looking at the synced data too? Why would they need to recover the password? Encrypting the mobile database would prevent this.