I used to be an instructor. Someone will take the 3 of you (most places won't touch 2 yo) but it won't be the best.
One of the main differences mentally I noticed with adults v kids is expectations. Kids don't care if they spent a week lying on their back in the snow, or hitting things with a stick. If they want to stop, they stop. Adults are conscious (perhaps it's subsconscious!) they've paid X for the trip, and they want to be able to tell Margaret they did the blue run, and they don't want to be the rubbish skier. They put more pressure on themselves to succeed. Ironically, the kids almost always do better.
Then there's a whole host of physical difference. Children's centre of balance is much lower. If they fall, they tend to bounce. I taught for 5 years and had one child break a bone (he was 9 and an incredible skier already, fell on a jump). Most weeks at least one adult in ski school will fall and break something (although often when they're not in lessons but practicing independently in the afternoons 
). As such, children are less scared of falling and often see it as fun.
Children often don't have the physical strength to run skis parallel until they're around 7 years old, so spend far longer in snowplough/pizza, which is a comfortable position for them. For most adults, the pressure on the knees and thighs in snowplough is painful so they want to run skis parallel asap.
Then there's what you can do as an instructor. With a 5 year old, for example, is often take them up the drag lifts between my knees. If they got tired or there was a tricky bit of piste I could ski with them laid back on my legs between my skis. I can use reins with the more maverick wild child style kids. I can ski backwards and catch them if they can't stop. There's no way I can take an older teen/adult between my skis or catch them at speed, it'd knock me (and them!) over!