Greetings, dear SBC (peace to you!), and how the heck you been? My responses would be:
Would you consider her father's actions immoral?
1. I would, yes, because it's a lie (that was not a "spanking"), inhumane (I wouldn't beat a dog that way), unnecessary (while perhaps bringing some kind of sick pleasure to Daddy probably did nothing to deter daughter in the right way), instills the wrong kind of fear (of being beaten vs. disappointing a parent because you love them and/or of suffering other consequences due to whatever "wrong" was done), etc.;
If not immoral, would you say his actions were unjust?
2. See above, and since I must assume that Daddy is a sinner, too, in some way, size, shape, or form... I would say unjust, as well;
If not unjust or immoral, how about unloving?
3. See above, and... in light of my reverence for the saying "All things you want men to do to you, you must do to them," and the knowledge that no one wants to be beaten for their wrongs, including Daddy (and Mommy)... and the "security" a child is supposed to feel from a parent... I would say unloving, also.
You can also add lacking joy, peace, kindness, mildness, goodness, long-suffering... and certainly self-control. Meaning, no "fruit" of the spirit. As a christian, then, I would have to reject it as a display of the fruit of the flesh: anger, reviling, hatred, etc.
Of course, regardless of what I THINK... I would/could not judge this man. I would, if I knew him (and his wife SHOULD have, but, well, she apparently has the same issues)... speak to him... admonish him... and try to help him see just what took place and how "outside" of God... and God's will... it was. I would then tell him that he should try to do what he could to make it right with his daughter - explain himself... and ask her forgiveness.
If he tried to use OT analogy, I would refer him to Christ. If he tried to used the "spare the rod" analogy on me, I would refer him to the "rod" that Christ used... and ask him which one of his disciples did he beat... even when THEY disobeyed, displayed a lack of faith, and what have you. If he tried to refer to the overturning of the tables in the temple, I would ask him if he really thought Christ lined those ones up, say, told them to "lean against the wall and turn your bottoms out toward me" and then proceeded to lash them... or whether he thought that my Lord struck out with ropes... and anyone in the way may have gotten lashed, but certainly not enough to cry out, "Please... STOP!"
If he listened, cool; we're, golden. If not, I would ask a couple of others who knew him to go with me and speak to him, with the same goal in mind. Again, if he listened... cool. If not, I would pretty much speak to anyone else I knew, ask them to deal with it/him. If he listened... cool beans. If not... then he would be "like the world" to me. In that light, he would be at the mercy OF the world... and its "superior authorities." I wouldn't hate or shun him... but I wouldn't take a stance against such authorities FOR him ("This is OUR business, we take care of our own, etc.") - since he will have showed himself to be part of the world... then his conduct is their business... not mine.
All of this is based on my "christianity," of course... and possibly his. If, however, he rejects those, what can I say? He's a man of the world... and so the property of world, just as if he were my brother in spirit but chose not to listen to the admonishments I and others were trying to make. Again, then, it's up to the world as to how to deal with him.
how should god should deal with a parent who is physically abusive to a child?
God WOULD do it in same way He wants that parent to deal with that child: in love, peace, kindness, goodness, mildness, long-suffering... and self-control. Which SHOULD result in joy: for both God (or the parent)... and the parent (or the child)... as a result of the child being "saved" (or, in the case of humans, the parent, as well). And He would do it in the same manner as I stated above: talk to the parent... indeed, vehemently admonish him, first... and if he doesn't listen (which is the case, more often than not, since people "claim" to not hear Him), have others admonish him.
And if he still doesn't listen (which is odd, is it not, given that folks say the reason they don't obey is because they don't hear, yet hear might be some right in their faces... and still, they don't listen?), leave him to the world to deal with. As any parent who has a disobedient child (who's no longer an "infant" but at an age where they might need to be their own "master") should. If he can't learn from you... perhaps he will learn from the world. Which can be a MUCH harsher "teacher."
Which is exactly what the Most Holy One of Israel does: first HE speaks to us... through His Son... to turn back our way. Then, He sends others to tell/remind us, because we don't/won't/can't/haven't listened to that Son. Then, He lets us go our way... out into the world. Some of us learn our lesson out there... some of us don't.
Just curious, though: why ask "christians"? I mean, the similarities to John 8:6 aside, of course...
Again, peace to you!
A slave of Christ,
SA