Hi Rebecca and welcome to Cardiff. It's a great place to bring up children. My husband and I have recently moved here from London - back home for me as I grew up in Penarth.
Penarth is a great place for families - it's in the Vale of Glamorgan rather than Cardiff itself, but just the other side of the Bay, so very near, with excellent public transport connections into town. Schools are really good, and there are loads of young families. The beach is pebbly, but nice for strolls, as is the marina.
There's a good mix of types of home, with bigger (more expensive!) detached houses and gigantic, beautiful Victorian piles in Lower Penarth, more modern family homes out in Cosmeston and Sully: (might suit you if you're more car users), and modern flats and townhouses in the Marina (probably not ideal for babies and toddlers).
More Victorian terraces in town, and the 'top of town' area: this used to be quite run down, but now it has a view of the Bay instead of the docks and tidal mudflats, and they're demolishing the derelict Council estate, so this area is getting very popular now.
Good luck with the move and with the pregnancy.