I'd never want to discourage anybody from getting kids out in the woods. But I'd agree, no matter how biodegradable, animals will dig up any of that stuff. What a disgusting mess. I still can't believe how often I see TP just left on the ground. I do think there's ways to make it work, like you said, maybe having the dog carry them. When I did it with cloth, I'd dig a hole, and carry pans of water away from the creek to wash them. 6 times a day was average for him though, so it got to be a lot. But most kids aren't that frequent!
Here's my philosophical take on babies/kids in the outdoors. I've been a stay at home dad for 16 years. The biggest thing I learned from my kids when they were little was to scale back my ambitions to their level. I love reading about the great adventures on this site, have experienced a ton in the past and am really looking forward to a lot of them in the future. But when kids are young, they have this amazing passion for all the little details. What is a tiny trip to adults is an expedition to them. Camping next to a creek, a few hundred yards off a trailhead, or maybe staying in a cabin in the woods, they can show you swirls in the water, the fun of watching sticks thrown in racing down the creek. I remember our youngest at about 1 sitting in a meadow of grass, picking up flowers and seed pods and intently looking at them, touching, smelling for the longest time. Picking your way through some dense trees, building a little fort of sticks, throwing rocks in the water all can be an experience right up there with an Everest expedition if you see it through their eyes. It's a pretty amazing experience, and one that disappears pretty quickly. Then as they get older, they might just be up for longer expeditions every year.