No poverty is ok but in terms of understanding some of the root causes for poverty these are three key areas.  The target was around child poverty (admit it, it sounds nicer for the media, we are rescuing the ones who are innocent in all of this, it's palatable), which cannot be tackled unless poverty for the whole family is dealt with - as you say.

In work poverty covers both men and women, but again the effects of poorly paid, crappy part time work and lack of affordable childcare is proportionately more likely to effect women.

Ad astra per aspera