No, sorry, I misinterpreted your question... If I understand it correctly, I think the below should explain.
for that, Fredo, Bess, Grace, and Ringo are siblings:
Fredo - eldest Male
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Prince Gerald Princess Mary
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Prince Wayne
Bess - eldest Female
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Prince Tom Princess Jane Prince Don
Princess Grace (younger female)
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Princess Alia
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Prince Oscar Princess Adele
Prince Ringo (younger male)
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Prince George
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Prince Ed Princess Ethel
The Old Ways: Bess is Queen. Jane is the Heir. If Jane dies, Grace will be the Heir. If Jane marries a peasant, her husband will become a Prince. If Prince Tom marries a peasant, he will become a peasant.
The Law of Eagles (as Written): Fredo is King, Gerald is the Heir. If Gerald dies, Wayne will be the Heir. If Mary marries a peasant, her husband will become a Prince. If Prince Ringo marries a peasant, he will become a peasant.
The New Law: Fredo is King, Gerald is Heir. If Gerald dies, Ringo will be Heir. If Princess Mary marries a peasant she will become a peasant. If Prince Tom marries a peasant she will become a Princess.
Oversimplification I think that there are probably social norms against marrying people with a vast social rank gap.
My suggestion for a change on Law of eagles is: that it is a matrilineal patriarchy and marrying up works either way.
Fredo is King, Tom or Don is the Heir. If Tom and Don die, Oscar will be the Heir. If Mary marries a peasant, her husband will become a Prince. If Prince Ringo marries a peasant, his wife will become a Princess.