The kids walked up on XC-skis with climbing skins and the adults had an extra set of alpine skis/boots on and in the backpack.
Where were the kids alpine skis on the way up?
On our adult backpacks together with their alpine boots, helmets and alpine clothing for skiing down. They typically walk up in in XC-skiing clothing to not overheat. Yes it's a bit of a drag for us parents but it's a good workout and kind of eliminates the fitness differences. Our 10-year old carryies nothing, our 12-year old gets a 40L backpack with light stuff like helmets and her own snack and drinks. Otherwise, she has way to much energy...
Done this way it's no problem going 1000+ vertical meter as long as the track is soft and easy.
I actually have a pair of fritschi freeride that I could mount on her skis. But walking in Rossi 70 SC with heavy frame bindings would probably kill the joy of this for anything but very short tours. She has 60-70 ski days in a season but only 4-5 of those days will be alpine touring so touring boots and dynafit bindings doesn't make sense to us at this point. Perhaps in a few years.