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 
         |               |
Prince Gerald   Princess Mary
                               |
                      Prince Wayne
 Bess - eldest Female 
   |                 |                  |
Prince Tom  Princess Jane  Prince Don
Princess Grace  (younger female)
            |         
      Princess Alia 
          |               |
  Prince Oscar   Princess Adele
Prince Ringo (younger male)
            |         
      Prince George 
          |               |
  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.