paul--I'd definitely agree with being alone, and to me, that would be hard to do on a boat, unless you did a totally private cruise, and that would get pricy. The idea of snorkelling with an engagement ring and possibly losing it, would make me very leery of that! Another option might be a waterside table for an early dinner at a great restaurant in Grand Case. Beautiful view of the sunset and lights of Anguilla. ..or, if they are a more casual couple, feet in the sand at Calmos at sunset!

It might help if the original poster said exactly where the family is going to stay, as you may be able to walk to somewhere great on the beach. For example, there is a lovely point out by Flamingo that would be perfect, to me.. Mullet is also basically usually deserted by sunset, so long as you don't go on Sunday! Lots of great choices!