With a family of that size, I wouldn't worry about renting a house. I think you'd be much happier in a house than a flat. You'll also be more likely to have a garden (back yard) your children can play in.
By the way, I live in Cardiff too. It's a great city! One thing you'll love with a family is the abundance of park space in Cardiff. It's actually the greenest capitol in Europe thanks to the Marquis of Bute donating so much of his grounds to become parkland. Bute Park is lovely to wander around in and has some fun activities through the year. Roath Park is probably my favourite for families. It has a great playground for kids, a lake where you can row canoes and paddleboats, plenty of ducks and geeses, rose gardens, etc. You'll also have to make sure to take the kids out to St. Fagans, which is a great open-air living museum full of centuries old homes where you can learn all about how life was lived throughout the centuries--complete with millers, blacksmiths, cloth weavers, etc. It's one of my favourite places, and it's completely free (well, except for parking).
Anyway, if you need any tips or advice on Cardiff, feel free to PM me. I'll be happy to help out where I can.
