相互之间

Sits as a prepositional phrase between subject and verb: [group] + 相互之间 + [verb]. Slightly redundant in spoken Chinese — 相互 (xiānghù, 'mutually') alone usually does the job. The full 相互之间 is preferred in formal writing where the 'between'-ness needs to be explicit.

usage

Compare 相互之间 (between members of a group) with 互相 (hùxiāng, 'each other,' adverb modifying the verb): 我们互相帮助 (we help each other) vs 我们相互之间有竞争 (there's competition between us). Same root but different syntactic slots.