A SlatepackAddress is a bech32 encoded ed25519 public key and when shared with other parties is used to represent the ability to receive Grin transactions.
grin-wallet already handles ed25519 keys for the v3 onion addresses in Tor transactions. These keys can be extended to be a general SlatepackAddress to allow a universal key format for both transport and encryption that is error-checked, QR friendly and easily human identifiable.
Slatepack - Grin Documentation
So in other words, a slatepack address is a public key wrapped as a onion address. Since two wallets with same mnemonic have the same public key, they also share their slate-pack address. I am not sure if running two wallets with the same address leads to routing issues/a conflict. I can imagine it might. With the Grin CC wallet we also use two instances, and indeed I often lose my peers for reasons unknown to me. If such a problem occurs might also depends on whether you use Grin++ (gives me some issues when running multiple instances of the same wallet), or grin-wallet (rust).
Edit: Grin++ is introducing the option to generate a new slatepack address in the yet to be release version 1.2.8. Grin++ achieves this by generating a wrapped private-key derived with another account from the same mnemonic. In case you encounter issues with running multiple instances of a wallet with Grin++, you can generate a new adress for one of them once Grin++ 1.2.8 gets released.