Gangle. Been there totally. Have got to the airport and refused to get on the plane. But let me talk some sense into you.
You are flying with three kids. Flying is phyically draining and demanding - reduced oxygen and all that. So it is natural to feel funny and sometimes we muddle that up with 'I feel funny so something must be wrong'. No, just reduced oxygen making your heart race a bit and you feel dizzy. Get a relaxation tape and practise using it. Concentrate on deep breathing at take off.
Doing it with 2 small DCs is really hard work. So it is going to be tough - accept that, and ensure you pack everything you can think of that will help. For long haul with small kids I pack surprise presents to open every couple of hours - nothing big but just something fun to occupy them. TV good too.
I find travelling with the kids helps me stay in control as I don't want to lose it in front of them.
I use Arg Nit 30c and I swear by it. You can buy in in most chemists. As with all homeopathic remedies, take it into a clean mouth ie nothing to eat or drink apart from water 10 minutes before and after taking it. Take a pill half a day before, 2 hours before, 1 hour before, at take off and then as you need. You can't overdose. It's transformed my flight experience and quite often I fly no with no adrenalin surge whatsoever.
So accept it will be tough, practise relaxation and take Arg Nit. Remember it is only for a few hours and the benefit of getting where you want to is worth it. Good luck.