I love this idea!  I can totally related to management thinking of this in a vacuum and having HR think through all the details.  :) And although I have never worked with one of these -- typically companies who track attendance have 'no-fault' --I am actually working on crafting something similar with a client right now.  This is the new HR -- finding things that are important to the employees and making it happen.  I am using a bereavement policy as a template.  I suggest the following:

1.  Define Family.  We are including spouse, parents, children, and grandchildren and asking for documentation for each incident. 

2.  Conduct a brainstorming session with management and get a pulse on what type of incidents are 'excused' and which are not...Clearly define what type of incidents are 'family first' -- is it just medical incidents for things that aren't classified as FMLA (due to employees tenure) or can I call in 'family first' for a kid's dance recital and bring in the program?  Be as specific as possible.  

3.  Draft a policy.  Review with an attorney.  

4. Draft a form to request the leave (or add an option to whatever system that you are using now to request bereavement, pto, attendance, etc).  

5.  Have an employee focus group.  Ask them questions to understand what 'family first' means to them.  Ask for feedback on the draft policy.  Try to iron out any potential issues.  

6. Train the payroll/manager or whoever 'classifieds' leaves.  Anything in the grey should be sent to HR for review.   

7.  Everything should be tracked as an attendance infraction and then removed once documentation is received.  

8.  Keep a log of what incidents are being excused and denied.  If anything is even remotely medical related, give the employee info on FMLA. 

Best Wishes!