TF Torrance provides an account of the Latin reception of this term (perichoresis) with reference to Hilary, and - in the process - clears up the misconception that it is etymologically associated with the notion of dancing. The interpretation of the term with reference to dancing has some limited merit, but it is an interpretive move as opposed to an etymological explanation. In the quotation below I am transliterating the Greek terms on the fly: see Torrance's text for the precise forms.
Thomas F. Torrance, The Christian Doctrine of God: One Being, Three Persons" (Edinburgh: T & T Clark, 1996): 169-70.
"Hilary was very familiar with Athanasian and Cappadocian theology which he learned during his exile in the East, and although he wrote in Latin he clearly had in mind the Greek terms and chorein and choretikos in this account of the way in which the Persons of the Holy Trinity reciprocally contain one another while remaining what they are in their otherness from one another. Here we evidently have developed the full concept that was to be given technical expression in the term perichoresis (perichoresis), which like the verb perichorein derives from chorein meaning both 'to go' and 'to make room for' or 'to contain'.*"
*Footnote #8 opens with the following sentence: "Choreo is not to be confused with choreuw which means to dance as in a Greek choros or chorus."