More information is needed, but if the child is in need of immediate medical attention and the other parent is refusing to provide or procure care,...

Yes, it can be a crime to record a confidential communication without consent. PC 632. There are noted exceptions however. See, e.g., PC 633.5....

Will the other party stipulate or agree to continue the earlier hearing? Speak with a local attorney.

Are you scheduling things during the other party's time? Speak with a local attorney.

It's unlikely to be known unless you bring it up. Though these questions are anonymous, it's probably best to stop posting about this online.

If he said he'd "redo it all because he [k]new it was wrong," then it sounds like he acknowledges the problem. You're likely left with deciding...

What do you mean by "conservative"? Inland California is more politically conservative than is the coast.

What do the court orders say on this point? Speak with a local attorney.

Why not just take the deposition? Speak with a local attorney.

Withdrawing the subpoena would likely make the motion to quash moot.