EDIT: It is really down to the original questioner, je crois, to ask his girlfriend to clear it up. The best I can offer is that it’s likely something along the lines of:

• I can’t offer you my car. I want her not to offer you her car.
• I won’t be able to give you my car. I want her not to give you her car.
• I won’t give you a ride. I hope she won’t give you a ride either.

Si nous acceptons «titine» as «voiture», c’est simple. Mais @joel a indiqué dans les commentaires qu’il croit que le contexte pourrait être «insinuation sexuelle» [or should I just say «double entendre» here?], alors …

Certainly in English we make occasional puns on “ride” to mean both a car and sexual activity, but I’m not able to speak for whether that’s currently normal in French. But, a search for “French slang” and “titine” …

Google says boobs.

Er, I’ll rephrase.

I found this answer from Nawaq at the wordreference.com forum which suggests that titines can be used to refer to, well, norks¹.

Sein(s), poitrine (normal word), nichon(s)/nichonaille/nichonnasses, loloches (plural), boobs (the English word), eins (verlan de seins, always used in the plural), nibard(s)/nib(s), tétés (from téton “nipple”), obus (these are really big breasts), nénés, miches, roberts (not sure it’s still used, really old), pare-chocs (I love this one but it’s quite “offensive”), mamelles, pis (these are for cows “pis de vache”, I picture a very old, not so pretty pair of breasts), airbags, titines, tétines, balcon (y a du monde au balcon, a generous pair of breasts), if you want to say something to a woman who have small breasts you can say that she’s a “planche à pain” or that she has “oeufs au plat”. gougoutte(e), lolos (childish), loches (I think these are big breasts “t’as vu cette grosse paire de loches ?!”), if you like fruits you can also say “ananas” and “pamplemousses” but it’s not really slang I think, it’s mostly old-fashioned (it comes from a song — funny), melons, flotteurs (old-fashioned too), roploplos (old-fashioned too, sound really funny), micheton(s), signes extérieurs de richesse, boules, meules, tchoutches… there must be a ton of others but I think I’m gonna stop here.²

But again, I can’t say for sure which meaning is intended.

This is difficult to answer without context – but I have heard ‘titine’ be used to refer to a dummy (British English) or pacifier (American English).

It is a contracted form of

une tétine

People here have confused the word Titine with the word tetine.
Tetine means teat or dummy.

Here titine probably means car, people who really like their car usually call it titine.