Lufthansa complaint: poor service, costs of flight changes, having pay new covid tests and just overall poor experience

My kids were due to fly out from manchester to seattle, Luftansa cleared kids to fly but in airport Luftansa advisors said could not fly without birth certificates, we then had to pay for 2 new flights 2 days later that cost 350 pound. 2 days later when was due to fly, at luftansa check in we was told the agent we paid 350 to hadn’t transferred booking over so they needed to call and get it manually changed, the service agent kept on telling person on phone needed to hurry as gate was about to close, unfortunatley gate closed and kids missed that flight, we incurred going back and forth to manchester airport over the 2 days costing alot petrol, we faced having to then pay 100 pound when kids flights was changed to fly from London instead of Manchester, as kids was upset my wife had to pay 100 to fly to London with them, we faced near 80 pound in parking tickets, we also had to pay 200 pound to get new covid tests done for the kids to fly 2 days later, it was just horrendous service over the 2 days, Your manager in airport told us to contact you as we should be refunded 350 we paid on flight change, we should also be reimbursed all other costs we incurred and compensation for poor service. I made this complaint at end June, and contacted use twice since and still not recieved a response or a refund.