Of the areas previously mentioned, if a train station is important:
Whitchurch, Rhiwbina, Heath, Radyr and Taffs Well all have train stations with regular trains in to Cardiff.
Gwaelod y Garth is walkable to Taffs Well station, as is Tongwynlais (and there are several buses from Tongwynlais)
Pentyrch & Creigiau have a bus service in to Cardiff. You'd need to drive to Taffs Well or Radyr stations to catch a train though.
Whitchurch, Rhiwbina and Heath are very bustling and prosperous areas of N. Cardiff, shops, restaurants, pubs, takeaways, libraries etc.
Radyr is smaller but still has a parade of shops, various cafes, library, doctor's surgery, restaurant, a small bar and then there's a pub, garden centre and farm shop on the outskirts (between Radyr & Morganstown).
Taffs Well has a co-op, a few pubs and some takeaways.
Gwaelod y Garth has an excellent pub, and a dual stream bilingual school, and is walkable to Taffs Well for a shop.
Pentyrch has a village shop, a butchers, some salons and a couple of pubs.
Creigiau has a Tesco Express, a couple of pubs, an excellent farm shop.
They are all very different villages/areas and you'd really need to visit and get a feel for them.
I'm inclined to agree with some previous posters though, and suggest that your best compromise might well be Abergavenny, in terms of commute for both you to Cardiff and your mum for childcare...