I'm recently back from Fuerteventura with 3 kids (a 4 yo and 16 wk old twins). We stayed at the Oasis Dunas which was great for families. There's a Kiddies Club for kids from 4 and a creche from 6 months old. There's entertainment every night which the kids love. The pool is the largest in Corralejo, I believe.
It's about 10 mins walk from the main restaurant area with some great restaurants (try Jaipur if you like Indian), and the beach. It's beside the Waterpark, and there are supermarkets only a few minutes away. If you are planning on stocking up on stuff for the week, a trip down to the Spar (a real supermarket, not the Irish convenience store variety) in the old town is worthwhile (about a half hour walk).
The 2 bed apartments themselves are decent, if basic enough, but then that seems to be the way in most of Fuerteventura. Each bedroon has 2 single beds. There's no a/c, but you can pick up a fan for a week for €12.
Personally I'm not that fond of Lanzarote, and find Fuerteventura much more chilled out.