Are two keys derived from the same password vulnerable to a related key attack?
Unless the key derivation function you use is specifically designed to exploit related-key attacks, then no, it will not result in a vulnerable related-key pair. It is true that XSalsa20 is not designed with related-key attack resistance in mind, but a key put through any decent KDF will not lead to exploitable weakness.

This answer explains the kind of effort that can go into creating a pair of related keys. Suffice it to say, there is absolutely no reason to worry that a KDF will produce such keys. The only other kind of attacks occur for certain ciphers when keys are extremely similar. An example of this is RC4, where encrypting known-plaintext with multiple keys that differ in only a few bits can lead to complete key recovery.

Note: I have not analyzed your overall password management scheme, just your direct question about related keys.