This may require you to be rooted, or it may just not work on your device (some phones behave differently than others), but something like this would do it:
Profile: Dump Most to Voicemail
Context: Time 08:00 - 13:00
Context: Phone Ringing [Caller: !Mom/Husband/Son/Daughter]
Task:
End Call
This will dismiss calls from any caller whose name doesn't match Mom, Husband, Son or Daugher (see pattern matching in the Userguide for more information). If the rings at all before unwanted calls are dismissed, you may need to add the following:
Profile: Silent Dump to Voicemail
Context: Time 08:00 - 13:00
Enter Task:
Default Rintone [Type: Ringer, Sound: Silent]
Profile: Audible Callers
Context: 08:00 - 13:00
Context: Phone Ringing [Caller: Mom/Husband/Son/Daughter]
Task:
Play Ringtone [Type: Ringer, Sound: <preferred sound>, Stream: Ringer]
These will set the default ringtone to silent during specified hours, but when a call comes in from either Mom, Husband, Son or Daugher, the <preferred sound> will play (and stop when the call is answered or dismissed).
This is untested and may require a little tweaking, but it should be pretty close to what you want.