so....
if your daughter was on the aircraft with the blown tyre would you have preferred her to have been ferried across the Atlantic for 7 hours with no real knowledge of the possible damage to the aircraft or losing the ability to hold for a while to figure things out, if the gear didn't drop back down.
The fact that you got to heart of the subject (compensation) by the end of your first sentence tells all. How much are you hoping to claim for this peril you suffered?