Neglect can alternate with periods of authoritarian control.
Overruling her decisions, ridiculing her in front of the children, portraying himself as the only legitimate parenting authority.
Browbeat suggests the persistent application of highhanded, disdainful, or imperious tactics: browbeating a witness.
Cow implies bringing out an abject state of timorousness and often demoralization: a dog that was cowed by abuse.
To bully is to intimidate through blustering, domineering, or threatening behavior: workers who were bullied into accepting a poor contract.
While children must respect his authority, their daily care is the mother's responsibility, especially routine or less pleasant duties such as diapers and homework.
He may be unaffectionate with children and find excuses to avoid coming home.
He is unlikely to sacrifice his needs to meet family responsibilities.
His praise and attention, so rarely bestowed, may be highly valued by children.
This material is summarized from Lundy Bancroft & Jay Silverman (2002).
The Batterer as Parent: Addressing the Impact of Domestic Violence on Family Dynamics. If an abusive man involves himself in child discipline, he has rigid expectations, low empathy and an angry style of "power-assertive" (i.e. Discipline is a quick fix to an immediate problem, not a thoughtful strategy based upon reasonable and age-appropriate expectations.
He may see himself as a superior parent and not listen to input from his partner.
He may swing between authoritarian and permissive, even neglectful, parenting.