Arabic dialect↔English machine translation remains difficult due to extreme dialect variation, inconsistent orthography, and limited parallel data. Moreover, dialect translation is often needed in remote regions or by economically-disadvantaged communities, which often operate in compute-constrained or offline settings. Motivated by these concerns, in this paper we explore optimizing Arabic dialect↔English translators that run over small LLMs, which could be implemented on small offline devices. We show that reasoning-oriented reinforcement learning can substantially improve small multilingual LLMs for Arabic dialect translation. Using the MADAR corpus, small Qwen-2.5 models trained with a think-then-translate template and optimized with Group-Relative Policy Optimization using a SacreBLEU reward outperform a much larger 7B baseline trained with supervised fine-tuning. The dialect-to-English BLEU score more than doubles from 17.4 to 34.9, while the English-to-dialect COMET score improves from 0.57 to 0.73.