Many people fly with anxious pets and they use some medication to help them chill, and things go well.
Can't think how many times I've flow with a screaming baby on the plane or they guy sitting next to me snoring so loud you could not hear the announcements. Not the mention the toddler who kicked the back of my seat from New York to Germany
Get your pup some meds from a vet and let them sleep,on the way home.