I am building an app for children which has some popular fairy tales in it, like, the little red riding hood, Goldilocks, the ugly duckling etc. The stories will be in our own words and we are originally creating illustrations for them. If we publish the app and sell the app for money, will we be violating someone's copyrights?
There is no copyright in an idea. A retelling of a story could be a derivative work, and the making of it a violation of the author's rights to authorize the creation of derivative works (17 USC 106 in US law. article 2 of the Berne Copyright Convention).
However, the originals of most "fairy tales" are long out of copyright, and new versions of them may be created and published in any form, for pay or not, by anyone who chooses to do so.
Some "fairy tales" are in fact original creations recent enough to still be under copyright protection. (at most 95 years in the US for works published before 1978, 70 years after the death of the author in many countries). In those cases a new version would probably be a derivative work, and require permission from the copyright owner.
In some cases a particular author added significant elements to the plot of a fairy tale or folk tale recently enough that the version which introduced those elements is still protected by copyright. In any such case, a new version or retelling that included the new (protected) plot element might well be found to be a derivative work, and so require permission. Basing any retelling only on versions clearly out of copyright will avoid this problem.