Something like this:
" INSERT INTO ChildArchive (foo, bar, baz) " & _
" SELECT ChildTable.foo, ChildTable.bar, ChildTable.baz " & _
" FROM ParentTable INNER JOIN ChildTable ON ParentTable.ID = ChildTable.ParentID " & _
" WHERE ParentTable.Date " & _
" BETWEEN #" & Me.UserDateField1 & "# AND #"...