How can I delete an app where no one realises I have downloaded it? Basically there are apps which I will download, like Instagram, and delete it when I’m done for the day. But when I go back to the app store there is a cloud and an arrow on it which means I have downloaded it before but I don’t want that therefore my children not to see it. Is there a way of me deleting the app without it showing that I have downloaded it before?
There is no way to hide the download. You can hide it from the purchased list but the cloud will still appear.

A solution:

Give your kids their own Apple ID’s, change your Apple ID password and device password.