It only happened once in Bakemonogatari when Araragi went on his first date with Senjougahara (and her father). Araragi called her by her family name Senjougahara, and Senjougahara teased Araragi and asked if he call her or her father. And then Araragi called her by her given name (Hitagi)
They're dating, so why they don't call each other by given name? Does Senjougahara do this out of respect to Hanekawa?
Even though we viewers have spent three, four, five years of our lives watching Monogatari, Koyomi and Hitagi have only been dating for about a year at the end of Monogatari Second Season. In other anime, characters who've known each much longer than that are still on a family name-basis; for example, Honey and Clover takes place over four years, but by the end of it, almost everyone is still on a family-name basis. That's something we should probably consider.
Not only that, Hitagi herself is a distant sort of person. Look at the lengths she went to to stop anyone getting involved with her when she was afflicted by the Heavy Crab—she alienated her friend, Suruga, and actually cut open Koyomi. Because of her past, she's distant and standoffish with everyone, but she's especially uncomfortable with romantic matters. She warns Koyomi early on in their romance (Tsubasa Cat Part 2) that it's going to move very slowly if he stays with her, and that she might never be ready for certain intimate activities. I'm sure she wasn't including calling each other by given name in that, but it's still a sign of the very slow progress that she warned Koyomi about.
I also think we should look at Koyomi himself. In general, he seems to use pretty respectful forms of address. He calls every one of the heroines by family name, even though Mayoi and Nadeko are younger than him and could probably be referred to by given name, possibly with -chan. (In Love Hina, Keitaro Urashima calls Motoko Aoyama "Motoko-chan" from the get-go, and even though she despises him, she never calls him on this that I can remember.) He calls his own sisters "Karen-chan" and "Tsukihi-chan" with an honorific, which Tsubasa remarks on as odd. He refers to Oshino Meme as "Oshino-san", even though Oshino is a weird transient in a Hawaiian shirt and Koyomi doesn't seem to find him particularly worthy of respect in most ways.
Given all of the above, it seems likely that:
As for Hitagi hassling Koyomi when they're in the car with her father, well, that's Hitagi. She loves making him uncomfortable. It might also have been a way for her to try on being on a given-name basis in a non-threatening environment without committing to anything. If she liked being called by her given name, she could ask Koyomi to keep doing it; otherwise, once she's had her fun, they're back to family names. I don't really think she keeps this up out of respect for Tsubasa. I would go too far into literary analysis if I talked about all my theories on the dynamic between Tsubasa and Hitagi, but suffice it to say, I don't think Hitagi ever saw Tsubasa as a loser who she should be a gracious winner towards, which is the view that that kind of gesture would suggest.
In Japan, it is normal to address others by their family name instead of their given name far longer in any kind of relationship than in the West. First name basis is usually reserved for very close friends, and even then not always applied, depending on the people involved and their background.
With that premise, what can be observed is not very unusual, just sufficiently borderline to allow giving a spotlight to the issue in the story.
The way Senjougahara uses this to tease Araragi can be considered her trait. She often (ab)used similar situations in the same manner and made a pun of it, which confirms the image and personality she displayed before.
