I have a theory that, basically, after Pink faked her shattering, The Diamonds decided to replace her with a new, upgraded Pink Diamond, who would still bear the original design idea and character (hence the clownish vibes), but would be more serious and Diamond-like, but eventually she came out too serious, maybe she wanted to take over the Great Diamond Authority, or maybe The Diamonds just decided that nothing could replace the original Pink, and, well, eventually they poofed her and decided not to speak of her again (kinda like what happened with Eclipsa in SvTFoE). And now, she somehow broke away from her bubble and wants revenge from both The Diamond Authority, and Steven (yes, please, read this sentence exactly the way they say "and Steven!" in the theme song), whom she mistakenly treats as Pink Diamond, the whole cause of her creation and eventual suffering (frankly, she's not the first one). Another Idea of mine for the reason of her invasion is that because she was "programmed" to think that she is Pink Diamond, she thinks that Earth is rightfully hers, and so she's gonna invade. I can already forsee the ending - Steven and the Gems have a talk with her (after a battle, of course), and tell her that she doesn't have to be Pink Diamond, that she can be herself, just like Steven once did. And she eventually drops the Pink Diamond identity, and becomes friends with Steven and the gang. On a sidenote, I think I used the word "Diamond" a little too much in this post.