Is trust in a relationship not just important but also an essential part?

The question describes Ayn Rand's affair with NB as "informed," which seems to refer to the fact that Ayn Rand, unlike nearly all other participants in extramarital affairs, insisted on she and NB informing their respective spouses of their intention to have an affair, and even obtaining their spouses' consent to do so. Ayn Rand lived up to that principle, while NB blatantly failed to do so, "cheating" on both Ayn Rand and Mrs. B in a second concurrent affair. This cannot properly be described as a breach of trust by Ayn Rand. (More information on all of this can be found in The Passion of Ayn Rand's Critics, by James S. Valliant, which includes an extensive collection of material in Ayn Rand's own words, from her private journals, posthumously released for publication by Ayn Rand's Estate.)

Ayn Rand's approach (an informed affair) illustrates the proper principle for anyone who feels the need, as Ayn Rand apparently did, to enter into an affair with someone else while already married. (See also Ayn Rand: A Sense of Life, by Michael Paxton, pp. 142-143.) Still, if the question is fidelity rather than trust, and what even an "informed" affair would do to the original relationship psychologically, even if the spouse consents to it in advance, then I can see considerable room to wonder. Yet Ayn Rand's own marriage clearly survived her painful experience with NB, and Ayn Rand and Frank remained together all the way to Frank's natural death in old age.

Most people who cheat (even NB) simply do it without discussing it in advance with their spouses. That certainly is not condoned by either Ayn Rand or Objectivism. At the very least, it's a breach of contract; and an uninformed affair cuts far deeper than that psychologically.

It should also be noted that Objectivism regards sexual love as a major value in human life, not to be treated lightly or casually. For Ayn Rand, her affair with NB developed in exactly thay way, even though NB's role seems to have been very different in motivation, and thoroughly value-abnegating (as Valliant's book explains)..