Sandy:
My first suggestion would be to upgrade to SPServices 2014.01. You're quite a few versions back. BYW, you can use the listName (like "Tally") rather than the GUIDs. It makes your code more portable, and certainly easier to read and maintain.
I think the problem probably lies in your list structures. I'd be surprised if it were to work differently in different browsers.
Your Nations list should have a Tally column which is a lookup to Tally.Title if you want that cascading to work. You're storing the relationships for both Tally - > Gate and Nation -> Tally in the Tally list, which isn't fully relational. The SPCascadeDropdowns function needs to see the parent -> child relationship list unambiguously in each relationshipList.
M.
My first suggestion would be to upgrade to SPServices 2014.01. You're quite a few versions back. BYW, you can use the listName (like "Tally") rather than the GUIDs. It makes your code more portable, and certainly easier to read and maintain.
I think the problem probably lies in your list structures. I'd be surprised if it were to work differently in different browsers.
Your Nations list should have a Tally column which is a lookup to Tally.Title if you want that cascading to work. You're storing the relationships for both Tally - > Gate and Nation -> Tally in the Tally list, which isn't fully relational. The SPCascadeDropdowns function needs to see the parent -> child relationship list unambiguously in each relationshipList.
M.