We’re back and forth to Mallorca a lot. Flight time there is approximately 1 hour 50 minutes from LGW . Where will you be flying from? It is a nice short flight and good for a first flight for your children.
I am ex Cabin crew and DC are 7 and 12.
Definitely do not cancel. I have the most horrible anxiety disorder but amazingly love to fly and it doesn’t bother me but I fully understand anxiety and how debilitating and crippling it can be.
I know it because I too have it.
My children are great flyers but then they do it a lot , so are used to it.
You say your children have never flown and this is part of the problem- the unknown.
I would try to determine the trigger- is it being up in the sky/ fear of crashing / claustrophobia/ can’t get off/ plane sounds etc?
Definitely go to the Drs appointment and see what/ if any medication can be given.
Talk about the worries but don’t force your child to look at planes.
The flight radar app is good in terms of seeing in reality how many planes are in the sky. You can type in your route- and look at the country you are travelling over to get there.
Talk about it as being a mode of transport. Literally that.
What are you doing when you get there?
Where are you staying?
We do lots of snorkelling there ( my children recently saw a huge octopus 🐙) .. you could talk about swimming, the food , hotel and things you are going to see and how exciting it is going to be.
Headphones are great for the plane. They drown out engine aircraft engine noise and are good for watching a screen too ( films/ music etc - definitely take this ).
This might be something to consider.
Talk to staff on the gate pre boarding ( they may possibly speak to the crew and then they’ll be really aware of how your child is feeling when you board and can offer support).
We don’t fly back for a few weeks - shame we aren’t out from the same airport on the same day.
Good luck.. pm if I can be of any more help.