No. The fact that you are pointing out each individual makes this a bit special. like a one-to-one relationship. I've found this that answers all our arguing:Then, would we ask about the relations among Mary and her mom and her sister? Is that what you're saying?
There is a persistent but unfounded notion that between can be used only of two items and that among must be used for more than two. Between has been used of more than two since Old English; it is especially appropriate to denote a one-to-one relationship, regardless of the number of items. It can be used when the number is unspecified <economic cooperation between nations>, when more than two are enumerated <between you and me and the lamppost> <partitioned between Austria, Prussia, and Russia — Nathaniel Benchley>, and even when only one item is mentioned (but repetition is implied) <pausing between every sentence to rap the floor — George Eliot>. Among is more appropriate where the emphasis is on distribution rather than individual relationships <discontent among the peasants>. When among is automatically chosen for more than two, English idiom may be strained <a worthy book that nevertheless falls among many stools — John Simon> <the author alternates among modern slang, clichés and quotes from literary giants — A. H. Johnston>.