The Many Faces of Ovoid 'Omeletta' Robotnik

AOSTH Eggette I feel would be something like Robotnik Jr, but unlike Robotnik Jr, she would be an actual organic person like Robotnik himself and therefore be loyal to Robotnik no matter what and would be a regular in the series and often helps Robotnik insult Scratch and Grounder for their failures. She would also be praised more by Mama Robotnik for getting into the Robotnik world domination business at such a young age compared to her uncle Ivo. (And she would also say 'I hate that hedgehog' like her uncle, though the I is turned into 'we' in the cases where Robotnik is present.)

SatAM on the other hand would be likely just as cruel as her uncle Julian, she was brought to the kingdom of Acorn with Robotnik when he fled from the Overlanders and was kept hidden until Robotnik's takeover where she began to receive lessons from Robotnik and Snivley and would also be a regular in the series until the final doomsday episode. Though instead of retreating with Robotnik, she would go with Snivley and would continue Robotnik's legacy, that is if Sonic SatAM had a third season.

The Classic Eggette and Modern Eggette would follow her uncle's plans as well and not much else to say other than she is a loyal little devil, though Modern Eggette would be a little more mature and less impulsive than her younger self.

Boom Eggette might be a bit more of a dumbed down version like all the other Sonic Boom characters to make way for comedy, though she is still loyal and instead might have a crush on Tails because of how brilliant and cute he is.