It depends on what you want to convey.
Let's look first at the adverbial clause "while we were there". If you are placing the situation in a past time with the perspective that the situation is finished, with a sense of psychological distance from it, "while we were there" would be rendered "mientras estuvimos allí". Placing the situation in a past time with a sense of reliving or observing inside that time, "while we were there" would be expressed as "mientras estábamos allí".
Now let's look at the main clause "It hardly rained". At first glance, this is a perfective simple past form in English (cf. "It was hardly raining", an imperfective simple past form) so we might be led to think that we should use the preterite in Spanish. But consider a sentence like "I chewed gum as I walked along the beach watching the sun set." "Chewed" and "walked" are typically considered perfective forms but this sentence is conveying the same imperfective ideas expressed in "I was chewing gum as I was walking along the beach watching the sun set" except with more ease. So we can't always rely solely on the form of a word to give us perfective or imperfective meaning. And we have to ask ourselves what are we really attempting to express in English before trying to craft a Spanish analog.
If we write "Apenas llovía mientras estábamos allí", we could be mentioning the simultaneity of the scarcity of rain and our presence at some place in the past without viewing the events within temporal bounds, or we could just be setting the scene, as Capt Spanish discussed, with a generalized sense of lack of precipitation during our stay someplace in the past, again without temporal boundaries.
"Apenas llovió mientras estábamos allí" features an instance (or maybe even a discrete number of uncounted instances) of barely noticeable rain during the time we were somewhere; this use gives focus to the rain conditions.
"Apenas llovía mientras estuvimos allí" again gives background information about the precipitation conditions while we were someplace, but the time frame of these conditions is referenced as completed in the past.
"Apenas llovió mientras estuvimos allí" could carry meaning practically identical to "Apenas llovía mientras estábamos allí", that the condition of scarce rain extended throughout our stay somewhere, however the events are viewed as demarcated and completed in the past. It could also refer to an instance of minimal rain during our stay somewhere in a demarcated, completed past time, again bringing focus to that event of rain.
There may be other interpretations as well and it would be best to hear from a native Spanish speaker about frequency of use and naturalness of these phrases. I've tried to cover non-exotic uses.
Note that you may want to reserve "mientras que" for situations where "while" takes its oppositional sense and means "whereas". See the DPD, entry #3 under "mientras" at
http://lema.rae.es/dpd/?key=mientras.