Error on covid test resulted in overseas flight missed and extra expenses for new tickets, covid test, etc

My son was booked on a flight to Nice, France on the 1st September 2021. We had a test done by the Shelly beach Lab 30 August 2021 that was necessary to board the flight to show he was negative. He could not board his flight as the lab spelt his name incorrectly and it has to be the same as on his passport. When the test result came back we only looked at the "'negative" status and did not think to double check their work as they are suppose to be a reputable company. The manager and marketing director Brenton Sassman assured me I would be fully refunded for all other expenses incurred. New ticket, new covid test, etc. A month later they say they will only pay back the test we done with them. This is unacceptable. I sent all the invoices necessary to confirm the unnecessary expenses incurred, I demand to be fully refunded for all the expenses incurred because my son could not board the flight. Enough emotional trauma was experienced on your error. The least you can do is to reimburse the extra expenses incurred.