I'm a native speaker, and we use "get ready" in exactly the way you describe.
Even though we sometimes qualify the phrase by saying: Get ready for [some event], that "for" clause can be omitted when the listener already knows where we are going. In other words, although get ready can mean different things in different contexts, I can still usually say:
C'mon! We're leaving! You need to get ready!
and that will be understood to mean: put your shoes on, brush your teeth, comb your hair and look presentable, etc.
The precise meaning get ready will vary, depending on where we are going. So long as the hearer knows where we are going, I don't need to add the, say, for your piano practice. For example, I have teenagers at home, so, for me, it works very much like this:
10 or 15 years ago, though, whenever I said, "Let's get ready" to my wife, that always included "Make sure we have the diaper bag!"
You needn't worry about get ready being misconstrued to mean "brace yourself for some bad news" or "get into your starting blocks." Those are very specialized meanings that people wouldn't even think about, unless they were in a situation where that would be the meaning that makes the most sense.
For example, if you wanted your picture taken, and I was holding your camera, I might say, "Get ready..." – which doesn't mean, "go put on your shoes," or, "brace yourself for some bad news." It simply means, "Get ready, I'm going to snap the picture now" – so you should probably just give me your best smile.
Best Answer
I have a half-answer. I have seen that phrase (or one very similar) used, but not to mean "if we involve someone in other activities, he/she will stop what he/she is usually doing".
I have seen it used to mean, "Don't talk with your mouth full." And there is really no other way of saying it that I know of.
One example source (Word doc; see page 8):