In-car conversational AI is becoming increasingly critical as autonomous vehicles and smart assistants gain widespread adoption. Yet, existing datasets fail to capture the spontaneous disfluencies such as hesitations, false starts, repetitions, and self-corrections that characterize real driver-AI dialogs. To address this, we introduce DiscoDrive, a synthetic corpus of 3500 multi-turn dialogs across seven automotive domains, generated using a two-stage, prompt-driven pipeline that dynamically integrates disfluencies during synthesis. We show that DiscoDrive is effective both as a training resource, enabling DialoGPT-Medium and T5-Base to match or exceed KVRET-trained models on the MultiWOZ 2.2 and Schema-Guided Dialogue (SGD) relevant test sets (BLEU-4 improvements of 0.26 to 0.61; METEOR +2.10; ROUGE-L +3.48; BERTScore F1 improvements of 1.35 to 3.48), and as a data augmentation resource in low-resource scenarios, delivering additional gains of up to BLEU-4 +0.38, METEOR +1.95, ROUGE-L +2.87, and BERTScore F1 +4.00 when combined with 10 percent of KVRET. Human evaluations further confirm that dialogs sampled from DiscoDrive are rated higher than KVRET's human-collected dialogs in naturalness (3.8 vs 3.6) and coherence (4.1 vs 4.0), and are perceived as more context-appropriate than leading post-hoc methods (such as LARD), without compromising clarity. DiscoDrive fills a critical gap in existing resources and serves as a versatile corpus for both training and augmenting conversational AI, enabling robust handling of real-world, disfluent in-car interactions.