The shrewd King Abdulaziz ibn Saud likely would have conquered The Trucial States (UAE & Qatar) with ease if it wasn't for the British. Back then the House of Saud generally maintained a smart strategy of not angering the superpower of the day after the collapse of the first Saudi State where the Ottomans damn near annihilated them and brutally executed their leader (then referred to as an "Imam") in Istanbul. The Trucial States belonged to the British, as did Yemen so they were a no-go and Oman was strong in its own right and not worth all the trouble.
Abdulaziz likely would have united all of Arabia otherwise. Though, to be fair, the logistics behind conquering a heavily sedentarized Yemen seemed difficult to him even when his nation had modern artillery and motor vehicles in the 1930s and they quickly pulled out due to not wanting to anger the Italians in the Horn whom the British made clear they would not protect the Saudis from if conflict broke out between the two. However, they did take
Najran and
Jizan which the Yemenis are still salty about to this day.