The Aruban is BEHIND LaCabana they used to be "together" but are now separate. They are a 5 minute walk from eachother - if even that much. A gigantic parking lot is what separates the 2.
You can however, go over to LaCabana and eat by the pool at the Islander Grill - great lunches. I think they have pizza by the pool as well. There are a couple of restaurants for dinner at LaCabana but they are not the "best" the island offers - they are ok and they are very close to you.
Also for dinner you are very close to Adventure Golf and Alfredo's but there is a very busy road to cross to get there. Take a peek when you are there and see if it is do-able with the kids.
Alfredo's is very basic Italian food - huge portions great prices. Adventure Golf has lots of stuff for the kids to do and it attached to Alfredo's. Just make sure there isn't a BBQ bash going on at The Black Hog Saloon (also attached) it gets pretty wild, your kids' eyeballs will be hanging out of their spinning heads.
The bus is right outside LaCabana/Amsterdam and will take you to the supermarket. Although, I am not sure which side of the street is the right direction. Most people bus it to the supermarket and cab it back with their bags. Usually cabs waiting outside the market. If you think you can handle the bags feel free to get back on the bus.