What is the grammar in "don’t you dare"?
The grammar pattern don't you try to do something, which is used quite widely in English and of which the expression don't you dare do something is just a variant, is an emphatic way to say don't even think about trying to do that where you're placing extra stress on the fact that it's probably not going to be very wise of you if you try to do whatever it is that you're planing on doing. Whereas don't try to do something sounds simply more like a command or request urging you not to do something. Take a look at these examples:
Don't you worry about it! I'll get the books to you on time!
Here, I'm telling you that you should not even think about being worried that I will be late delivering the books to you. There is no point in being worried that you're not going to get them. In other words, rest assured that you absolutely will get them.
Don't worry about it! I'll get the books to you on time!
This one sounds exactly the same as the previous example with the exception that it sounds a little less emphatic. That's really all the difference there is between these two examples.
"Don't you dare ____!" is imperative. It instructs the listener not to do something.
"You don't dare _____!" is descriptive. It says the listener is afraid to do something. It also sounds weird; the usual form is "You wouldn't dare _____!"