Airlink no refund

We booked two tickets with my autistic daughter and we got to the airport on time. The guy at check in told us the flight is leaving soon so they can’t take the bag, I must speak to the security at boarding, they rejected the bag coz of the size and took their time until the flight left us. They told us to buy another ticket and had already booked a return ticket. No refund what so ever. Couldn’t even book another flight with that money. Whereas other flights like Flysafair allow you to book with that amount and add the difference if there is.