The mobile app now allows those with access to multiple sites to switch sites in the mobile app without having to log out and then log back in using a different login.
Note that your profile (on the web app) will need to have "Master Admin (can switch sites)" set to "Yes" to use this feature:
If that's set to "Yes", then you can switch sites by doing the following:
Tap the round user icon on the top right of the Dashboard screen.
Under "Active Account", tap "Switch Site".
Tap to select the site you want to view.