And now for some real input from a trainer qualified with enough stupid certificates, degrees in sports physio, weightlifting, powerlifting and triathlons and results from State - National & World Championships, than you can fill a wheelie bin with.
CORE STABILITY has recently been added to the fitness industries " Marketing Department " as another ploy to make money
!!!!For those non open minded people or textbook bandits who dont understand what Real World training requires to get real results - you may find it interesting that it coincided with the
Marketing release from the
STARS .... wait for it... of Pilates ! yes youve all been sucked into the money making vacuum cleaner

Pilates was by its original design only intended to teach at most - 5 people at one time !!! because its very hard to activate these stabilisers & you cannot effectively control a larger group of people (how long does it take a physio to teach '1' person to isolate & switch it on & off...)
Mikeayb was Partially correct on his exercise of squats (executed properly) but done with a Manta Ray pad that load spreads weight on shoulders not spine. The later induces another set of problems. This exercise utilises the Core stabilisers very efficiently
Kiteing uses compound movements with both fast N slow twitch muscle fibres that cannot be simulated by carpet munching

exercises
A
Reputable open minded Trainer or Sports Physio of great personal
Integrity should be able to use their imagination to efficiently simulate the various movements required by kiteing - including WTF - yes, jumping off a small bench to teach synchronisity of knees & balance for landing (naturally feet will have to be angled)
So in short

if your going to spend dosh on a fitness regime, make it specific so it works for you !
You wouldnt buy a trainer kite if it was massive boosts you were after would you

Ps I still recomend that cup of cement with breaky is by far the quickest way to Harden up them core stabilisers