Essentially, was the Reconquista about having the Muslims convert to Christianity or else? Why did the Spanish kingdoms want to conquer the rest of Spain?
(I apologize if this was asked. I searched this sub and read a few wiki articles on the subject before submitting.)
The Reconquista lasted nearly eight centuries. Attributing a singular motive to the whole period is never fruitful.
Evidence for the dominion theory is the fact that the various Christian kingdoms within the peninsula were often at war with one another. But that just means it's true of many specific leaders; it's hard to argue that Isabel I wasn't motivated, in part, by wanting to convert the entire landmass. But the real answer is, ask a more specific question if you want an answer more helpful than "sometimes!"
The Reconquista wasn't one military campaign. It is a whole historical period.
The Reconquista wasn't about converting Muslims to Christianity. Muslim communities existed in Christian-ruled territory for centuries, long after their lands and cities had been conquered by Christian kings. These were known as Mudéjares (as opposed to Mozárabes, the Christians that lived, or had lived in Muslim-ruled lands).
The Christian kingdoms saw themselves as heirs to the Visigothic kingdom conquered by the Muslims in the 8th century, but saw the creation of a single Christian ruled kingdom covering the whole Iberian Peninsula as more or a very long-term goal or an outright wish than as an immediate project. The whole of Iberia wasn't unified under a single crown until Philip II was crowned king of Portugal in 1581 after all.