I'm curious, is it really necessary to include the relay in that DM text? I mean if the recipient isn't sharing a common relay they won't receive the DM to begin with.
the sharing client should include relay information and the receiving client needs to be able to parse and follow that
many clients don’t support that yet (NIP19)
https://github.com/nostr-protocol/nips/blob/master/19.md#shareable-identifiers-with-extra-metadata
Discussion
What if the note you are sharing is from a relay that is not common with the sender?
common with the sender and receiver*
My point is the receiver won't see the DM at all if they don't have a common relay so it doesn't help to embed the relay address within the DM.
The relay you are using for the DM can be common but the note you are sharing can be on a relay the recipient doesn’t have. So they see the DM but don’t know where to fetch the note, which is what you described happened