Incarceration by itself is poorly correlated to the goal of reducing overall crime and reducing recidivism. Putting people in prison should be a last resort, instead of the first resort that the US and some other countries treat it as.

Regarding jail time for the wealthy, you're still thinking in simple numbers instead of means-tested comparisons. A more-wealthy person and a less-wealthy person that go to jail for 30 days both are physically restricted for 8% of a year. If you pretend that wealthy people earn the same way that less-wealthy people do (they don't), then both are naievely losing 8% of their income-earning time for that year.

It's still not fair, mind you—the wealthy person likely makes much or most of their money from diversified income streams that are less succeptable to temporary incarceration than the more-likely single salary-based income of a less-wealthy person.

Regarding the question of using children as leverage, this is addressed more intricately than I'll summarize here in contemporary cases e.g. with Elizabeth Holmes and the allegation that she, her partner and legal team have tried to lean on her having children as a way to attempt avoiding incarceration.