I also have around $500 per week for 2 children (primary age). We get by on it. I shop around, Cold Storage, NTUC, Giant, wet market/hdb shops etc. Sometimes money is tight but most of the time, we manage on that.
Are you given this $500 because you and your husband have agreed on this figure or is it all he'll give you? This is all we can afford really but we do manage to have a night out once a month or so (most of the time with the kids so we save on a babysitter!).
I think $500 is 'do-able', you just have to shop carefully. We've started having 'on-toast' night once each week (beans, spaghetti, egg etc). That saves money. A noodle night is a good one too.