I'm pretty sure the Emperor over the Sea is Emperor over everything, not just Narnia. Remember what Aslan said to the young Calormene in *The Last Battle*?
You're right, Peter was king only of Narnia and whatever lands they conquered. But yeah, time travel can make things confusing!
I recall from the books that their reign was happy, and I assume they were fair and just, and apparently quite beloved by their subjects. As for how the actual politics worked, not a clue.
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Peter was High King over all the kings and queens in Narnia, present and future.
Edmund seems to act as proxy king when Peter is away. He's the equivalent of a King Caspian.
As for the queens ->
Susan's role seems to be to be pretty.
If both Peter and Edmund are away, I'd assume Susan would be in charge, because she's older, but that's just a guess.
And you can't even explain Peter's role as being imperial, because Narnia already has an Emperor, over the Sea.
You're right, Peter was king only of Narnia and whatever lands they conquered. But yeah, time travel can make things confusing!