It's an authoritarian parenting style, and I don't think anyone really likes it. But there's nothing here to suggest any marginal physical or emotional abuse. I personally know a few traditional Mexican families where the father is addressed as "sir" as a sign of respect but still knows how to care for their children.
Really? from what part of Mexico? I'm Mexican and I've never heard someone addressing their father as "sir" (señor) not even "father" (padre) we usually use "dad" (papá), even using "usted" instead of "tu" is not common anymore. But then again Mexico is a really big and diverse country, so there must be zones where that could happen.
It's interesting because in some parts of Northern Mexico, you would think that use of "tú" didn't exist. NO ONE uses it, not even relatives or husbands and wife.
Hitting disobedient children is also a regional custom.
If your children respond to orders like trained animals or soldiers, they are doing so because they were conditioned to do so. I am choosing to define that conditioning as abusive because it simply doesn't happen naturally.
My dictionary defines abuse as "cruel and violent treatment of a person or animal". What is cruel specifically about setting expectations about what needs to be done? There is nothing cruel about requiring kin to call you sir especially when you can show that you deserve their respect.
It is plainly offensive to address kin as "sir".