Unless you wire the two-year-old's brain up to the one-year-old's so the two-year-old can stimulate the one-year-old's motor cortex, I don't see how that experiment would test my theory. (Maybe I explained it badly.)
Adults already show the one-year-old how to walk, encourage the one-year-old to crawl and try to stand, and so on – but the adults aren't teaching the one-year-old how to coordinate muscles. That's all the doing of the one-year-old. Some of it's instinctual (as it is in other mammals), and we have some relevant reflexes once you're actually up and standing (assuming you stay within their domain of efficacy), but overall, walking isn't instinctual for humans.
Consider physiotherapy in adults recovering from a nervous system issue. The physiotherapist has to guide the patient through exercises to rebuild motor coordination ability. (Some adults figure this out on their own, invent and practice their own exercises, and breeze through the physiotherapy, but in general physio is long and boring and arduous, because it's very frustrating and doesn't come naturally.) That's the sort of thing infants do on their own volition (with some encouragement from caregivers), but I don't see how it makes sense to say it's not their volition.