Solution 1:

Short answer

Yes, you can.

Modern grammars such as the Oxford Modern English Grammar show there to be a preposition, not an adverb. The preposition in cannot take adverbs or adverb phrases as Complements. It can take other preposition phrases as Complements. For this reason there is no problem using the word there after the preposition in.

When we use there with a stative verb, it has a general meaning of at that place. If you want to say something like in and at that place, you can say in there.


Full answer

In modern grammars such as Oxford Modern English Grammar (2011) or The Cambridge Grammar of the English Language (2002), prepositions are a class of word like verbs, nouns, adjectives and so forth which have specific properties. Although taking noun phrases as Complements is a common feature of typical prepositions, this is not a necessary feature of this class of word. So many prepositions like the word out often occur without a following noun phrase:

  • Bertha walked out.

This is similar to how, although many verbs take noun phrases as Direct Objects, this is not a mandatory feature of verbs. These developments regarding prepositions, have not filtered into dictionaries yet. This is likely to take many decades. Traditional grammars and modern dictionaries take words like out in the sentence above to be an adverb because it doesn't have a following noun phrase.

According to linguists such as Jespersen and Emonds and modern grammars such as CamGEL and OMEG, the word there is a preposition (some linguists think of it as a pro-preposition). It passes every test for preposition-hood and none of the tests for being an adverb.

It can appear as a Locative Complement of the verb BE:

  • She is inside the building.
  • She is there.
  • *She is locally. (adverb as LC, ungrammatical)

It can be modified by the specialised adverb right, which can premodify many preposition phrases, but cannot premodify adverbs in standard English:

  • It is right at the top.
  • It is right there.
  • *It is right locally. (right modifying adverb, ungrammatical)

It can be premodified by the specialised adverb straight, which can premodify many preposition phrases, but cannot modify adverbs in standard English:

  • Go straight past the traffic lights.
  • Go straight there.
  • *Go straight directly. (right modifying adverb, ungrammatical)

Preposition phrases can freely postmodify nouns, adverbs usually cannot:

  • that dog in the window
  • that dog there
  • that dog cutely (adverb postmodifying noun, ungrammatical)

We can usually use the adverb very to modify adverbs. We can't use it to modify prepositions or preposition phrases such as there:

  • *She lives very beyond the border. (very + preposition, ungrammatical)
  • *She lives very there. (very + preposition, ungrammatical)
  • She lives very locally.

All of this information shows that there is a preposition and not an adverb.

The Original Poster's question

The original Poster says that prepositions cannot usually take adverbs as Complements. This is a good rule of thumb! But it might be better to think about prepositions in the same way we think about verbs. Some verbs don't take Complements. Some verbs only take noun phrases as Complements. Other verbs cannot take noun phrases as Complements, but only take preposition phrases and so forth.

The preposition until can take adverb phrases as Complements:

  • until recently

However, the preposition in cannot:

  • *in locally (in plus adverb, ungrammatical)

However, the preposition in can, of course, take preposition phrases as Complements:

  • in from the cold

For this reason we can use there as a Complement of the preposition in:

  • in there

The word there means something like at that place when it is used with stative verbs. If you want to say something like at that place and in that place, you can just say in there.

Solution 2:

The word there could be used as either an adverb which doesn't require a preposition and a noun which means

that place / that point.

(You need to note some other dictionaries classify it as a pronoun)

The sentence could be rephrased to

It was cool and dark in that place (the reptile house).

You should note that there could be used with many prepositions such as 'up there', 'down there', 'out there', etc. The same applies to the word here.

[Merriam-Webster]

Solution 3:

Regardless of the nonsense about "there" being an adverb or a pronoun, read the original text:

After lunch they went to the reptile house. It was cool and dark in there, with lit windows along the walls.

At the end of the first sentence "they" are "at" the reptile house. There is no indication that they have entered it. If the text continued "It was cool and dark there", without "in", the reader would be left wondering if it was cool and dark outside the reptile house.

"In" is necessary to convey the full meaning of the text.