Hi Tinkerbellie
Only have 1 DS and we have flown twice with him - sadly 2 and under have to sit on your lap for take off and landing, but if there's a free seat (or you have paid for one) then they are on their own seat the rest of the time.
Buggy goes to the gate with you, but comes back via baggage reclaim (and that's a looooong way at Gatwick with an 11month old wriggler....)so would suggest some reins if 18month old is a competent toddler!
Top tips:
Make sure you have plenty of food and drink for the flight (provided that when you go you are allowed to take lots) so that they can drink on take off and landing - don't rely on the food being something your kids will eat and go with a bag laden just in case you get stuck/delayed.
Be aware that the changing facilities on planes are useless (2 year old with dirty nappy in toilet about the size of a shower tray - that was not fun!) and change before you get on the plane.
Most planes will give out some form of child enterntainement (crayons/colouring book) but its pretty meagre so have a load of books, games, cars whtever is small and reasonably quiet.
We flew with first choice, and they put the families together so mo-one without kids wasn't aware which little darling was having a paddy!! was very helpful!
BEST TIP!! Keep them on Uk time - that way they'll wake up a bit later and go to bed a bit later so you can go out for a bit in the evenings and feel that you're having a break.
GOOD LUCK!