Why does it need to fit between branches more easily? Does it hide, like a squirrel, by flattening itself on the top of a tree branch so that its silhouette is harder to detect against the branch? Does it need to walk along branches backwards frequently to escape predators, and the spikes would snag on branches? Does it live in very cramped spaces within its nest?
I'm not sure if instincts can "reawaken" like that. On the other hand, it's not implausible for the Pickaxe Tamow to actually have instincts to use vegetation for its dwelling, and the instinct has been modified here. (Adobe dwellings can be made using wooden posts or straw mixed into mud.)
"meant specifically for joeys to practice using their tails" That suggests they know to anticipate the joeys' needs, which is very remarkable. It's very remarkable that chimpanzees should store rock ammunition specifically to throw at zoo visitors for fun when the zoo visitors show up. Unless these are meant to be very intelligent for animals, it would be better to suppose the sticks are mere spandrels of nest construction, like crevices in archways once used to hold wooden beams in the archways' construction, and the joeys happen to use them in a way that is less risky than practicing outside. Or, perhaps, pregnant/lactating females are instinctively driven to add more sticks to the walls, because curious joeys tend to make holes in the nest wall, explore the holes, and then fall out of the nest to their deaths, and so whatever females were instinctively driven to add extra sticks made a barrier against joeys' curiosity and had more joeys survive.