Anguilla is a very expensive day-trip to attempt, particularly for a family, no matter how you do it but if you’ve never gone it’s so worth the day.
You can do a packaged daytrip through any number of companies that generally provide a r/t trip catamaran, sail or power boat trip with drinks and snacks and a stop at one of the out Islands or perhaps Rendevous Bay for lunch and a nice sail along the island of SXM.
And the other option is the ferry over either from Marigot $ or else somewhere near the airport $$, rent a car or take a taxi $$, drinks and/or lunch and possibly chair rentals while there or not $$$$ and lastly, departure fees from both SXM and AXA-$.
Don’t forget to bring your passports either way as they will be needed on both islands.