I have always found airlines to be reasonable with reasonable customers.
If you explain in advance that you are needed to assist your parents on flight and don’t want to annoy other passengers when you need to climb over them, they will get the point.
Never use your religion as a device to accommodate your whims; airline personnel are professionals and they will see right through you. And if you don’t get your way; so what? Be polite at all times and never ever create a chillul Hashem.