Children, that is, kept in by Barbara (6)
I believe the answer is:
Here is my best explanation:
'children' is the definition.
(baby is a kind of child)
'that is kept in by barbara' is the subsidiary indication.
'that is' becomes 'ie' ('i.e.' can be a synonym of 'that is').
'kept in' means one lot of letters goes inside another.
'by barbara' becomes 'babs' (I've seen this before. I am not sure about the 'by' bit.**).
'ie' inserted inside 'babs' is 'babies'.
(Other definitions for babies that I've seen before include "Storks' freight?", "Very young children", "Small children", "Infants" and "Recently born children".)