Devin Grayson’s writing of Nightwing was very damaging for the character - and included a whole lot of OOC moments both for Dick himself, and Barbara, since we’re talking about the matter. Their relationship began as they slowly overcame several issues that they had and Grayson went and took all of that down. The breakup made no sense; up ‘til Grayson picked the book Dick was never written off as a womanizer and he took all of his relationships seriously, and Babs isn’t an overly jealous woman. So, it was all sorts of messed up.
So, how to overcome it: Despite everything, they remained very close friends and still trusted each other. With time the rift was repaired - even if there was always an air of “what if” hanging around. They slowly began to flirt with each other, and while never romantically involved again you could see just how comfortable they felt with one another. Sadly, the reboot happened, otherwise (and this is a personal opinion really) they would’ve probably wound up getting together again (see Batgirl vol. 3 and The Black Mirror, or even Nightwing #153).
Luckily for you my friend (and for the shippers really), Convergence: Nightwing\Oracle #1 (coming out in April) states that they have become romantically involved again, so it’s a matter of seeing how that issue will play out!