"competing desires" is a correct and usable phrase in written English.
It is commonly used to describe situations where a person has two or more conflicting wishes or goals. Example: "She was torn between her competing desires to travel the world and settle down in one place for a stable relationship."
Mr. Agnelli balanced well the competing desires of shareholders and government.
Characters struggle with competing desires for thrilling unpredictabilities and the certainties of order.
At first blush, Trump seems to have squared two competing desires.
While Mr. Hatoyama has tried to accommodate the competing desires of the Americans and local residents, he finally had to admit that it could not be done.
Do you find that your religious vocation and your desire to write complement each other, or have the two ever felt like competing desires or vocations?
What he's referring to are the competing desires to put out fires, stop robbers, educate children -- and buy books -- and not raise property taxes.
The competing desire is not to look like an ignoramus.
He said he was torn between a desire for her and a competing desire — to work with her.
While waiting for the Normandy invasion to begin, two soldiers (Robert Taylor and Todd) muse over their competing desire for the same woman (Dana Wynter).
How does the University of Pennsylvania balance the competing desire to assemble a freshman class that has a diverse range of students from non-American countries, with what would seem to be the primary mission of serving an American clientele?
It surprises even Zhenya herself to learn how tenuous is her sentimental attachment to the idea of community action -- no match at all for her competing desire to shake up, if not to destroy, a home that has become for her a veritable prison of numbness and grief.
