Two kids from my child's parochial middle school were suspended for a day last week. I've seen many suspensions over the years, but never once an expulsion. One time several years ago (at another school, mind you) a half dozen families tried to force the expulsion of a kid for the frequent hitting that occurred. My child was one of the kids to get hit. But the principal pushed back extremely hard and took a ton of flak. She stood her ground, though in the end the family voluntarily changed schools.
Today in many liberal cities kids simply can't be suspended at all, period. In many other areas corporal punishment and suspensions continue to be used way too much. But actual results don't really track the way people assume they do one way or another.
What's the real difference between parochial schools and public schools? IMO it has little to do with policies or resources, but the fact that parochial schools demand parental engagement. It's often a prerequisite for admission. If the school knows the parent is engaged and working with the school, they'll often deal with behavioral problems that most public schools wouldn't or simply can't. By contrast, a friend of mine saw his entire public grammar school get shutdown by a self-identified radically progressive school board in Boston for failing to expel a kindergartner after a single incident (perpetrator, black boy; victim white girl; though really if anyone was paying attention the boy was arguably the victim, both by the ridiculous outrage, but also whatever was happening in his home life). This was at a school specifically created to mix rich white students with poor black students, and every family opted in to the experiment, and the school staff was simply following the gold-standard liberal policies the school was created for; policies which in this case were easily defensible, IMO. Its sad the way things went down, though the hypocrisy exposed was telling. People want to throw money at problems, virtue signal, and demand everybody else do something about these problems, only so long as they're not personally effected.
If the parent isn't engaged or can't be engaged, throwing more resources at the school won't help. If you want better outcomes, shift attention toward helping parents become more engaged. There are myriad ways to do that, and I really don't know what might help. But trying to fix the problem through school policies and resources isn't going to work. That avenue has been exhausted, though it still demands vigilance in maintaining appropriate resource distribution. Unfortunately, suggesting this kind of approach has categorically become a form of victim blaming--i.e. blaming parents for being poor.