My wife and I work for two different private companies.  Both
companies have insurance via Aetna but they have different open
enrollment periods. Thus, it is very hard to coordinate the benefits. 
We cannot shift from plan to plan depending on who has the better
coverage without having excess coverage.

Does the company or government define and govern what is "qualifying
event" for private healthcare?  If government, please provide a link
and supporting documentation.

Also would appreciate a recommendation.

The U.S. Department of Labor has the guidelines outlined under the
HIPPA regulations.  The website is:  www.dol.gov

The general rule of thumb for a qualifying event is:  Death of spouse:
 The surviving spouse and dependents are entitled to Cobra coverage. 
Divorce - spouse and dependent children are entitled to Cobra.  Loss
of employment, the employed spouse then has 31 days to enroll spouse
who lost coverage along with any dependents.  Birth of a child -
usually companies require notification within 31 days.  Marriage - 31
days to enroll new spouse.

If both employers offer Aetna, before the next open enrollment period
compare each employers coverage, i.e. - employee cost, co-pays,
pharmacy coverages, types of Aetna plans offered - PPO, POS, HMO, EPO,
etc.  Plan rates never go down they only go up each year.  Usually
larger employers can offer their employee's lower costs.