I feel like I should I should point out that the reason why Mama Robotnik hated Adventures Robotnik comes from the fact that he never beat Sonic, which caused her to be ridiculed by the other inhabitants of Mobius' Home For Really Weird Mothers. Game Eggman HAS actually beaten Sonic before in Forces and conquered the entire world, even if he was defeated in the end, so her hatred of Eggman would probably be far lesser.
... That does also mean she'd love Pre-SGW Eggman... Who I should probably mention is a different character than Pre-SGW Robotnik for those who don't know. Pre-SGW Eggman actually DID kill his Sonic... Via nukes. So she'd be impressed by his bloodlust and his willingness to go scorched Earth... Then annoyed that he refused to just nuke the Sonic of Pre-SGW Robotnik's world.