my best guesstimate about $200 per day will be more than plenty.
your children are not old enough to run up a huge bar bill (even soft drinks and virgin frozen drinks can cost lots)
if you eat out every "other" night, dinner for the 2 adults will run probably less than $100.
the 4 yr old and 18 mo won't eat much and will be able to eat small kid sized portions and kid priced.
the activities that your family of 4 will do will NOT be high priced SCUBA or sailing adventures.....more like butterfly farm visit, donkey sanctuary visit.
maybe a babysitter will cost more than you want to spend, but could be money very well spent.
so, IMO $200 a day is more than enough!