I'm not sure automatic password detection is available. After all, computers don't really have that function. You still have to select the user/enter username.
As far as having the option to lock certain apps automatically when in family mode but unlocked in My mode, upgrade your Android version at least 4.3 (newest is Lollipop 5.0 but that's not available across all devices yet- 4.4.4 KitKat is widely available).
This will give you access to a new profile/user type: Restricted Profiles.
From Google's help pages:
About restricted profiles
As the tablet owner, you can create restricted profiles that limit the
access that others have to features and content on your tablet. For
example, you can create restricted profiles to prevent family members
who may have access to your tablet from viewing mature content.
You can use restricted profiles for several purposes, including these:
- Parental controls. Selectively restrict family members from accessing mature content.
- Kiosk. Set up the tablet to demonstrate selected apps and features to customers.
- Retail. Let customers explore tablet features, but prevent them from browsing or playing games.
- Point of sale. Limit employees to the use of selected sales and register apps.
To set up a restricted profile:
Note: You must be the tablet owner to create a restricted profile.
- Touch Settings > Users > Add user or profile.
- Touch Restricted profile, and the new profile with a list of settings displays. To name the profile, touch New profile.
- Using the ON/OFF toggles and Settings , select the features and settings you want to grant access to.
To set up the new profile, press the Power button to return to the
lock screen, then touch the new profile icon.
When the restricted user finishes setting up, the Home screen is
empty. The granted apps appear after the user touches the All Apps
Edit a restricted profile
Note: You must be the tablet owner to edit a restricted profile.
- Touch Settings > Users.
- Touch the profile icon.
- Using the ON/OFF toggles and Settings , select the features and settings you want to grant or deny. The changes take place in real time.
Important: If you turn off an app, the profile user loses all content
associated with that app. If you grant access again, the content isn’t