App control another app
If you are using consumer devices, one option is to use Android for Work or other Enterprise Mobile Management software which supports Android.

See: https://developers.google.com/android/work/requirements?api=clouddpx#35-silent-app-distribution

IT admins can silently distribute work apps on users' devices without any user interaction.

Or look at this StackOverflow post: PackageInstaller "Silent install and uninstall of apps by Device Owner” - Android M Preview which is off-topic for this group.