OP has asked for a process to get satisfaction, but it looks to me like parent and son arrived at the destination and made the court date and had some luggage delivered late with one still missing.

So, if I am reading this correctly, it looks like the actual "loss" is the delayed luggage. OP should expect reimbursement up to the EU limit for baggage items purchased to cover for what was not delivered once the delay reached the length of time provided in that law. Personally, I would just buy the required stuff and send the bill. Nothing is to be gained by sitting waiting for pre-authorization to buy the stuff. That just reinforces/proves that the stuff is NOT actually urgently required. If you need the stuff, you need it, so buy it, then stomp your feet to get them to pay the bill. When they refuse, resubmit and demand an explanation. When they offer an inferior amount of money, demand an explanation for why the full amount is not given. Keep on until they pay. But don't sit back suffering without necessities waiting for them to give their blessing because I would not expect them to leap forward and offer help.

If AC had to compensate passengers for individual employees from time to time providing clueless information, speaking rudely, and creating stress where no stress was needed, we would be millionaires and they would be out of business. Experiencing rudeness and stress is not a compensable "loss".

The terms and conditions when you check in for the flight clearly say to put your medication and valuables in your carry-on so I don't know what to say that is helpful. I personally have put things in my checked bag that I later realized I should have carried on (like all my gear for a marathon the next day), and I understand how a passenger who is flustered (e.g., heading across the world to go to court) can overlook the fine print, but AC will rely on the fine print. They did warn.

What I am surprised about is not protecting a child traveller in IRROPS. I realize it was not an unaccompanied minor but I thought that parties with children were in the category of vulnerable travellers they would try to get to the destination.

That said, in a court order situation, I would have booked the flight a day earlier, not just to allow for this kind of thing, but because of all the airport-closing terrorist nonsense that is going on in Europe, the occasional nasty volcano, storms, etc. If the court is not inclined to take those as legitimate excuses, then you need to build in your own insurance. (Or buy On My Way? Is that a thing OP could have used?)

I hope the rest of the trip is better.