The behaviour I would like to disable is shown in the following animation.
It has been reported as a bug in various places, and a topic of multiple discussions:
Although the current direct solution is to re-compile from a modified source, many recommendations have been made to the Nemo file manager: http://www.webupd8.org/2013/10/install-nemo-with-unity-patches-and.html
Nemo will fix the problem you have, but it won't be the actual nautilus, as it was a fork from an earlier version.
It seems fairly easy and painless to install, so giving that a try may be your best solution currently. (Assuming you don't want to rewrite and recompile nautilus. I don't have personal experience with Nemo.)
Your bug should be fixed in the future though, if the bug reports are of any truthfulness.
As of Nautilus version 3.17.91, this bug has been fixed by adding an option to disable the "auto-open" behaviour. From the NEWS file:
Major changes in 3.17.91: ... * Add a preference and disable by default automatic opening of folders while hovering on drag an drop operations (Carlos Soriano)
The default was subsequently changed to "enabled", restoring the "auto-open" behaviour for anyone who doesn't disable it explicitly.
Unfortunately this change wasn't in time to make it into Ubuntu 16.04, which ships with Nautilus 3.14.3. Ubuntu 16.10 shipped with version 3.20.3, so it and subsequent versions should have the option (at least until GNOME decide to remove it again in order to streamline the user experience).
I don't know whether this option is exposed in the GUI, but would expect not. In any case it should be possible to disable the behaviour from the command line with
gsettings set org.gnome.nautilus.preferences open-folder-on-dnd-hover false