If the author is looking for ideas here, with minimal impact on the existing design, I'd recommend putting the most-recently dropped animal in the back to allow for cycling through which one you pick up.

Another possibility is a "hover" state when when you mouseover a node with 2 animals, they animate quickly into a side-by-side orientation so you can easily pick which one you want to interact with.

Did you manage to? I couldn't choose the other one. (I forgot which one it was.) Even now on desktop it keeps picking up the dog and can't choose the rabbit.