ばばあ (babaa, "old woman", "hag") is usually a derogatory term for old women, similar to English "old hag". (Fandom Touhou's Yukari is infamous for being triggered by the phrase). It is possible to use it to refer to one own's mother though, though it will be quite rude and derogatory. Usually it is only seen in insults ("Shut up, old hag!" being the usual one when a boy gets sick of his mother's nagging).

That said, like all insults, it is possible to use it semi-affectionately, if the other party accepts. In that context the severity of babaa gets downgraded to something like "old lady". That said, any person who regularly gets away with using babaa directly to their mother's face will definitely appear to have a rather interesting (in the rocky sense) relationship. It will definitely be very... out-of-place if you see it in real life. Especially in public, in front of others. Anime-manga-game-fictionland is a far different story though.

Though here above Mohawk Guy is just ribbing the Kid. He's not seriously asking him to call Momdroid that. Though I've no doubt he will be laughing in stitches if the Kid actually took his "advice".

There's also くそばばあ (kuso-babaa, "shitty old hag"), an even more derogatory form of the above.