I wanted to still give you information about switching between Facebook accounts on the same iOS device. As long as this other account is active anywhere on your device (via the Facebook app or your web browser app/s), it is the one your DoubleDown Casino app will connect to when you choose "Sign in with Facebook." It is this active login that is preventing DoubleDown Casino from accessing the other Facebook account you'd like to play under.
To help with this, please try the following steps. I know some of them are similar to steps you have done before, but please try to complete them again.
1. Delete the Facebook app from your device (this is only temporary; you can download it again afterward)
2. Next, open the Settings app and scroll down until you see Safari and tap it
3. Here, scroll down and tap Clear History and Website Data —If you have another browser on your device, such as Google Chrome or Mozilla Firefox, you will need to make sure that you've logged out of Facebook there as well
4. Launch the DoubleDown Casino app
5. Tap the gear icon in the upper-right of the game lobby to open the settings menu
6. Tap Logout (you may need to tap “Log out” again on a second screen)
7. Tap Sign in with Facebook and enter the credentials and password for the desired Facebook account
After performing all these steps, you can redownload and log in to the Facebook app if you’d like.