I know that you can upgrade a childs ticket for an adult one. It does not have to be partially used at all. There was a period of time, last year I think, that the Disney Stores here in Ontario only had child tickets. You could buy one and then upgrade at the parks. No problem at all.
Sorry, I have no idea about upgrading to a DVC AP. I have a pretty strong feeling that you can do it though.
Upgrading a child's ticket, to an adult ticket, can be done.
However, for no additional cost, it can only be done for a child who has now become an adult (Disney's definition of an adult, 9 and older). ie, you buy a ticket for a child who is under 9 years of age, and on a future trip the child is now 9 or older, you can upgrade it to an adult ticket for free.
If an adult tries to upgrade a child's ticket that was never intended for a child, you will likely have some trouble and be required to pay the difference between a child and an adult ticket.
Cheshire's sticky explains it quite clearly.
ETA: Note that if an adult could buy a child's ticket, and upgrade it for free to an adult ticket, everyone would be doing it to save on ticket costs. It's simply not permitted to be done (without paying the difference in price) for anyone else except a child who has now become an adult.
If the only intention is to save airmiles, you can upgrade the ticket at Disney. But, you will have to pay the cost difference from a child ticket to an adult ticket (plus other upgrades) if the ticket is intended for an adult.