'shuffled between' is a correct and usable phrase in written English.
You can use it to describe movement from one place to another or when someone or something is being transferred from one person or thing to another. For example: The cards were shuffled between the players before each round.
His legs wrapped in heavy braces, he would steady himself against the wall as he shuffled between rooms.
Mastroeni himself probably didn't even know his best position – he frequently shuffled between central-defender and holding midfielder.
Most parts of the human genome are shuffled between generations, making it hard to sort out the pattern of inheritance.
(A Real Housewife, on the other hand, might be shuffled between multiple public relations agencies before landing a seat).
Athletic directors have shuffled between the two tournaments, stepping from the present to the future and back again.
Researchers can analyze the ancestry of admixed populations because of the way the hereditary material is shuffled between generations.
More remembers when Bedford's body arrived at the company's HQ in 1991, after 24 years of being shuffled between cryonic facilities and storage lockers.
My experience would have been improved by not being shuffled between various workers who made me repeat my background information over and over again.
For one thing, three-parent situations typically involve a couple and a third person living separately, meaning the child will get shuffled between homes, and this raises problems.
Her novels sketch a circumscribed scene whose anchors were the church and the vicarage, and the busy, decent Englishmen and -women (more women) who shuffled between the two.
On the train, small, silent screens set at the front of the cabin shuffled between ads for MasterPass, by MasterCard, and English headlines from the morning's news.
