I agree with everyone else, the situation probably just got more dangerous with the baby on the way if they find out her true identity because their baby is technically the true heir to the throne... if word gets out it just spells trouble for their family.
I believe her mother also said that when they come to overthrow the king, the whole royal family will be killed as per usual. So Edna might have similar thoughts.
There’s also the idea that she was forced to act like a prince her whole life, if she’s happy where she is and feels much more free why would she want to change that by telling her secret
I just realized that she is the reason why the current king is existing so...Why was she hiding her identity again? ┑( ̄Д  ̄)┍