I'm at the awkward age with kids where I want to start taking them on more adventurous outings, but they're not quite ready yet. I took my 11 year old on her first backpacking trip last summer. She had the energy to hike in about 1.5 miles.
Was she carrying too much weight, could you take half of her load? My 6 year old can easily hike 1.5 miles, so I'm thinking for an 11 year old it must have been weight or crazy terrain.
I carried most of it. We weighed her pack at 10-15lbs if I remember correctly. I felt it was appropriate at the time.
It was a slight uphill. I think it was mostly because it was an uncomfortably warm day.
If you know to expect 1.5 miles, find a hike where there's something cool in 1.5 miles. That's on you, to do the planning so the weakest member of your group has fun.
Our kids are now older, but some things we did with them:
Loads of walking when they were small. Some hikes. Our first (and regular: once or twice/year, sometimes with friends) backpacking trip with them was a SHORT access hike: something like 1.5 miles (and, er, 1500 vertical feet) up a mostly dis-used trail into a hanging valley that hardly anyone knows about. So for the cost of a 45 minute drive and a bunch of challenging hauling of gear for the parents, we got into a mostly-empty backcountry valley. Some years DH made two trips to get all the stuff up there. (Some years we were carrying an toddler, along with all the camping gear for our family...)
They did a bunch of camps focused on wilderness skills, and we learned what games were played there. Once we got to our backpacking site and got set up, multiple rounds of "predator" were played. (It basically involves sneaking up on "it" -- the first round you have to hide yourself so "it" can't see you, then "it" closes his/her eyes and you have to try to sneak up and touch them. If "it" points directly at you (because s/he can hear you) you're out.) We spotted stuff (fish! plants! mushrooms! once, a Moose that was way-the-heck too close!). We hiked nearby "peaks" in the range that surrounded our valley. We lay out at night and spotted stars and planets. We let the kids do all the talking they wanted, and took advantage of the opportunity to hear what they were thinking about without distractions. We let them wander off and have alone time, if that's what they wanted.
We also took our kids on twice/annual ski trips to backcountry huts. Again, the parents hauled immense loads when the kids were small, but it meant that once we got there we had plenty of food, some games to play, a kid-sized potty seat (they have outhouses ... and in our defense, we only did that once, when a kid was potty-training at just the wrong moment..) After the kids were no longer tiny we stopped towing them in, but they had a deal with my DH who was pulling a cargo toboggan -- he'd tow them on the flat sections, they had to walk (it was snowshoes at that point) on the steeper bits. We hauled in their downhill ski gear, so they could ski out. Ultimately, they were upgraded to various versions of backcountry gear, so they could go up and down on the same equipment... Some years friends came with us. Some years, friends and their families came with us. A couple of times the weather or situation turned bad, and we had to turn around.
The moral of this storytelling: do whatever you need to so that it's fun for the kids. Make up stories and tell them around the campfire! Invent appropriate-scale adventures. Haul ALL the stuff yourself: the recommendation is that kids should start out carrying less than 10% of their bodyweight, and if that's too much, they should drop down further. Make very sure that they have what they need to be comfortable (yes, for small kids this means carrying an entire change of clothes in case they fall in a creek). Make sure there are ample tasty treats. Train ahead of time with them, so that you (and they) know that they can handle the physical part. (There's a peak that overlooks our town, so we started out by hiking up that. With cookies!)
(Now our "kids" are 20 and 23, and on our Christmas hut trip in 2023 they carried greater than 50% of the weight. In fact, I handed off a (decanted, I'm not an idiot) bottle of wine to the older one halfway in, when he asked why I was sl slow.)