Can my landlord enter my apartment when I'm not home but my children are and they are all under the age of 18?

You need to review your lease.  If the landlord followed the provisions of the lease for providing notice prior to entering the apartment, then they have the right to do so.  If you are uncomfortable having your children in the apartment without you when the landlord is there, you need to make arrangements for the children to go somewhere else during that time or make arrangements to be there yourself.