.you must be mad, or else you wouldn't have come here

Then she gets reunited with Ten & it's all 'OMG I LOVE YOU OMG I MISSED YOU SO MUCH OMG I LOVE YOOOOU!!!!111' & her kickass factor just drops.
Ugh, you're absolutely right there. It's so clichéd (the old running-into-each-other's-arms-in-slow-motion routine) and so annoying! The only nice thing about that scene was Donna's smile, as I know she has always wanted the Doctor to be able to see Rose again.

Besides the temper tantrum when Rose gets returned to Pete's universe with 10.5, it also annoys me when she's with Sylvia and Wild watching the conference and Martha appears, and she throws her skreechy "Who is she?!" It reminds me of the "Doctor's Girls" wallpaper my Polly icon comes from, and makes me remember one of the reasons why my future Fourteenth Doctor fics is to be a multi-Doctor story: besides wanting to make the Short Doctors Club team up together (and having the three of them jam with each other's instruments of choice - Two with the recorder, Seven with his spoons, and Fourteen with her [cut for spoilers]), wanting to give a proper appearance to Thirteen and his companions (who until then only show up to regenerate or are mentioned in conversation - with Jamie meeting one of the companions between fics), and wanting Jamie to meet Two again, I also want Rose to be surrounded by past companions who meant a lot in the Doctor's life so that she can get a dose of humility, I want Mickey to be treated with a little respect, and I want Fourteen to pwn Ten at every given moment and to point out just why she thinks he's annoying.
And, of course, I want to play the Terrance Dicks card and insert some plot instances that might help explain some annoying plot holes from other multi-Doctor stories, since the Fourteenverse doesn't have Season 6B to correct those holes. But that's another story.

& then , as I've seen someone put it, she throws something of a temper tantrum when she goes back to her own universe WITH HER OWN TEN.
Actually, I don't think she was throwing a temper tantrum - she was in fact oddly rational when compared to how she would normally behave in those circumstances. And we should not forget that that's actually Pete's universe, and that her own universe is the one she once again left; equally, that's not her own Ten, but a clone like the Valeyard. Still, I think she got a best deal with 10.5 than she would have had by returning to the TARDIS with Ten, since he has some Donna kickassery added to him, and in some ways reminds me more of Nine than Ten, and needs her more the way Nine did - which means she can be awesome again while she's with him.

But at the same time, I think she would have guessed that the Doctor was no longer with UNIT (if she was keeping in contact with the Brig or Harry, as I TOTALLY believe she would have)
Actually, the Doctor has never left UNIT and is still in his payroll. Harry would probably not know about it, since by 1977 he was working for NATO. As for the Brig, I'm yet to see the two episodes of SJA where he makes a return (it's the only story from that series I haven't watched yet), so I cannot say if they're still in contact or not. But if they are, he would probably have told her about meeting Seven in Battlefield, which is meant to take place in our own time rather than when it was made, and so she would be aware of the Doctor still getting involved with UNIT, and of the existence of a feisty, ass-kicking assistant who glomped the stuffing out of the Brig. :P
And also, we don't know how many adventures Eight could have had with UNIT besides the ones that might have appeared in the audios; I'm definitely not counting the EDAs for this, especially after what they did to the Brig.