Should a person with more children get less jail time because more children will be left without a parent as compared to a childless person.
Since the financial impact is not the main consideration of jail time, it shouldn't be major factor.
With respect to children, children whose parents are imprisoned are more at risk of future problems, and so irrespective of other considerations it may well be preferable to society to take it into account.
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.
No. The point is that fines should be based on per-day income or some kind of similar measure of wealth. Which actually makes it consistent with the hypothetical economic punishments of being thrown in jail.
I was thinking of this in context of wars. Where people with children should be first to be send in front lines. With those with most offspring being higher priority. And those with none the lowest.
Jepodizing a business that employees people might will be taken into account.
Elizabeth Holmes seems to be counting on this one.
FWIW, both the country where I was born and the one where I live have chosen a simple approximation: Fines are set at "x typical daily earnings" and the court will estimate the equivalent in legal tender, jail time is set in days.