Banned for life? No. But if the club sacks him, I won’t shed a tear - the ‘hair-pulling’, as you put it (allegedly vigorous enough for her to end up on the ground, sustaining abrasions, while holding a 4 month old infant), is an escalation of his previous DV incident, where he punched a door to intimidate/express his fury at the same woman. I’d rather he be someone else’s problem when he gets to the Barba/Robert Lui stage of development, thanks all the same.
It’s very rare for domestic abusers to change their ways, unless something drastic happens. You do occasionally see people involved in a one-off that shocks them
enough to never do it again (if what you hear about AFB and his partner is true, one of those cases). Once the pattern of violent tantrums and lashing out at your domestic partner is established, though, there’s little chance it’s going to do anything but continue, and most likely escalate. The circuit breaker than needs to be something huge, either in terms of legal/financial penalty, or an abrupt end to the relationship, sometimes your kids hating you.
Hopefully his missus realises, and gets the hell out without wasting another decade or so, and bringing several other kids into the mess a la Ainslie Currie. That’s the saddest thing about the whole Barba saga - his girls are old enough now that they’ll realise and remember what he’s done to their mum, and it will affect them their whole lives. Get out while the kids are little enough, and it doesn’t have to be that way.
