You're right except for the fact that the baby on Gen1 is black (Bebitchi) and the baby on Gen2 is white (Shirobebitchi).Some help for Binary
Another telltale sign: On V2, going to the game menu will ask "game, shop, item," And I believe something else. Also Gen2 has slightly different characters, like the bad care teen
Kutchitamatchi=P1
Hashitamatchi=P2
Also, Gen1 (P1) has a white baby(?) and Gen2(P2) has a black one(?). It also has no genders and these are about the size of Tama Minis.