My family smokes at home but does not smoke when the kids are around, does the lingering smoke still harm young child?

Yes. Smoke anywhere in the home or car (even with the windows down) still gets to the kids increasing risks for all sorts of problems in them: asthma, sids (crib death), ear infections, sinus infections, reflux (gerd), and so much more. Kids can't get away from it if you don't let them. Smoke outdoors only, until you are able to quit.
Yes. Second hand smoke is dangerous for children and increases their risk of sids and respiratory illnesses such as asthma. If you have a family member who smokes as them to do so outside and change their clothes before returning inside. Smoke can linger for a long time on clothes.
Yes. Second and third hand smoke are very dangerous to children. If family members must smoke, it should be done outside only.
Yes. To understand what your kids smell in your home, quit for 5 days. The sensory nerves in your nose will regrow enough that you will be able to smell the lingeriing fumes on hair, clothes, closits etc. Those fumes lead to an increase in crib death rate, ear infections & other respiratory illnesses. The grearest gift a loving person can give to a child is the elimination of smokers from their life.