So how do user access the app? is it through hub? if so then when they open the app they will see all sheets in the App Overview screen. If you are planning to hide them even in the App over view screen then you have below options.
1. QMC --> Security Rules
Define 3 rules for 3 sheets in the published app on who can access what sheet.
Example : Sheet1 & Sheet2 from App1 should be visible to User 1 and User2
Sheet2 & Sheet4 from App1 should be visible to User 3 and User2
Doing this way you don't have to control using dropdown/custom mashup/extension.
This option will hide the sheets even on the app over view screen based on who logs in.