I will add my voice to the others advocating the water taxi. The Alilaguna is something to be endured; a water taxi is to be enjoyed. Make sure you have a map showing the exact location of your apartment. The driver may know of a dock closer than Fondamente Nove.
You have taken a giant step toward economizing in Venice by renting an apartment where you can prepare your own meals. The local supermarkets are well-stocked, but you should shop at the Rialto Market for seafood and vegetables at least once. You can take a traghetto across the Grand Canal from Ca’ d,Oro to Rialto Mercato instead of walking down to Rialto bridge.
If you do want to go out once, whether for lunch or dinner, I would suggest Rosa Rossa, known as Johnny Depp’s hangout while filming The Tourist in Venice. Yes, it is “touristy” but not in a bad way. Make a reservation is advance and they will treat you well. Your kids might like to sit in the room with Depp’s signed jacket on the wall.