I don't know if it can be depicted as slang. Really it seems like just any other normal word for me. Of course it's extremely colloquial but still, everybody knows and uses this word now and then.
As for rudeness of this word. Yes, it's kind of rude but not as rude as you can imagine.

The word is just another variation of conveying meaning of understanding based on the word дойти

Дойти is just to get to a particular destination while допереть is either to get to a particular destination with a lot of struggle along the way or to carry something to a particular destination with a lot of struggle (usually because you're carrying something heavy or hefty). Of course this struggle results in a very slow movement that impedes getting there easily and swiftly.

So I'd most likely use the word допереть instead of just дойти if someone hasn't been able to understand something for a VERY long time, especially if the thing to understand looks pretty simple. And I'd do that not to offend them but to add empasis and emotion to the phrase. Although it MAY offend people.

Kind of like that. I hope this helps