I assuming you are processing your mailing list through RE Mail.  If your using Export then this may/may not apply

I would think you will want to use "Mail only to constituents marked Head of Household".  You will need the 'with spouse addressee' field on the head of household record if it's not. 

Do you have an addressee format on records for 'the last name family'?  If not I'm not sure you'll be able to run this as one mailing. RE doesn't give the option to pull the last name field when processing labels. 

If you have several individuals living at same address with none marked as HOH, RE is not much help here.  To filter these out in RE you would need some kind of solicit code, attribute or constituent code to filter. 

It may be more efficient to export mailing list (include the addressee fields you want and the last name field) to excel or access. You can search for duplicates if needed.  You'll have a greater amount of flexibility in formating your labels.

My two cents...