Not going to go in to a lot of details, but has anyone here done this?  Is it even possible?  How do you go about it?

You don't?  It's a public health order, you can try to get an attorney to fight it or you can eat it and wait till you test negative.

I'm negative now.  This isn't regarding me, but a family member.  And it appears that you can:

    FURTHER, I DO HEREBY give notice that you have the right to seek judicial review of this Order in the State Supreme Court of the County in which this isolation order has been issued.
FURTHER, I DO HEREBY give notice that any such proceeding may be made by telephonic or video-conferencing means, so that you will not be required to violate this Order by appearing at an administrative hearing or in Court; and

I'm just trying to figure out how to do it.

Get a lawyer versed in public health law.  Call your local bar association for a reference to an attorney that specializes in that field.

Ignore it?  That’s the civil rights route.  Passive resistance

Agreed.

Probably won't find one in OP's County or the ones next to it.  
Call the Dept. of Health that issued the order and ask them which Judge hears these cases; I expect they've been told to go fuck themselves more than once.  

I spoke directly with the director of public health in our county.  She basically told me too bad, so sad, that even if I went through with the courts, nothing would happen before the quarantine is up.

Just for clarification, we're pissed because they quarantined my oldest son twice.  The first time, they based it off the date my wife tested positive.  This time, when I tested positive, they're basing it off of the date that I spoke to them, which only happened because I had to spend all day Friday and yesterday calling and trying to figure out when I can go back to work.  They openly admitted that if I hadn't and they finally got around to calling me in another week, for instance, then they would have quarantined my son starting on that date.  I have since tested negative because I have to test weekly for work since I'm not vaccinated.  I have to send the tests in no matter if I'm working or not.

As it stands, he's out of school for almost a month.  We know he had covid, he had the same symptoms the same time as my wife, but we tried to comply with the first quarantine order and didn't take him out to get tested, since we have common sense and knew what it was.  Now they're saying that we should have taken him out to get tested, but NOW, even if we took him out for a test and its negative, he can't go back to school any sooner.  

So TL/DR:  We would have done much better had my wife never gotten tested and lied to public health.  (Wife got tested because of a surgery she was supposed to have.  A friend tested positive so she got tested.)

just ignore it and go about your life

We can't just ignore it when he can't go to school, that's the whole point.

Correct, even if you had a lawyer ready to go on Day 1 of the quarantine order, by the time they filed with the court and the judge heard arguments on an expedited basis and issued a ruling, the quarantine would likely be up.

My wife has done a few emergency filings for clients on other issues and generally the best you can hope for immediately is an emergency stay preventing either side from acting and preserving the status quo until arguments can be heard and considered. These were largely done in cases where a dog was slated to be put down because of a bite incident and the owner was appealing the ACO decision and proposing alternative plans. In the case of a quarantine related to a "public health crisis" I wouldn't imagine that the court would issue a stay pending arguments. Your ass is going to remain quarantined until after arguments have been made and a decision issued, or the quarantine runs its course - whichever comes first. And as stated, that would likely be the quarantine running its course.

ARFcom Rule #3: "Never invite the Man into your Life."