You only need to enter information for any period of time where you had Obamacare or Marketplace insurance.  You will enter the information from Form 1095 A for this insurance.  You should enter the information only for the months you were covered by an Obamacare or Marketplace insurance policy.
 
For the months that you were covered by insurance offered through your mother's employer, you will only enter that you were covered by insurance. No other information is necessary.