Armature animation differs from IDE preview

Greetings, I'm trying to animate a cow and export it on a Blend4Web HTML (exam project), but baked animation differs from IDE since a bone doesn't rotate consequently from its parent and the parent bone rotates at the opposite side. To make it easier, I'll explain this with screenshots.
This is the cow before animation and its armature:


This is what I want (as displayed on IDE):

This is the output I get for this animation:

At this point, I thought the neck bone was rotating the opposite side and inverted it like this (IDE view):

But then the output was this:

Like only the neck parent bone rotates but the head child doesn't, so I've tried unchecking "Bake only deform bones" but nothing changed. At this point, my last attempt was also rotating the head bone like this:

and got this:

It looks like the nose doesn't rotate at all, and even if it would, I'm afraid the face would deform like that anyway. However I've tried to expand the head bone and reassign weights (not sure I did this well) in order to have the nose covered but nothing changed.
The weird thing is that in the same scene there also is a dog and the output animation for it isn't altered from what you see in the IDE.
How can I obtain what I wanted?

Hi, having a minimal .blend file would be helpful

Sure, here it is

Sure, here it is

You need to apply scale on cow and it's armature and all be ok. Before you have started to animate it's better to apply all scale on object that will be animated even armature.

Reply to post of user Mikhail Luzyanin
You need to apply scale on cow and it's armature and all be ok. Before you have started to animate it's better to apply all scale on object that will be animated even armature.

Thanks.
We weren't taught to use Blender in the course, I know this issue was probably ridicolous.