I love villa Camilla, one of my favorites. A couple of things about it though that may affect OP:
There are extra guest houses on property that may be rented at the time (they don't share the pool, but do share the property)
They do not take children under 5 years old because of second story railing and decking (don't know how old your kids are)
Views of beach are from second floor. Although technically beachfront and they own the property leading ip to it, it does sit back from the beach.
I think it's an amazing value for a terrific villa, but don't thi it addresses what the OP is trying to achieve. (I could be wrong, but thout I'd bring up those points)
Again, will you increase your budget or not be on the beach?
Aother thing to consider, very few villas in the hub (and those go for top dollar) which makes 90% of villas on island require cars to get around to supermarket, shops and restaurants. Didn't know if that was part of your budget