My beginning impression of this piece was indifference--it's a typical day, common in so many stories. But gradually, as it progressed, the tension mounted, and finally, the last line caught me quite off guard. The shift from peace to horror is nicely delivered. Wonderful impact (albeit only happening in the end).

I also liked the air of mystery with the dead man and the stubborn portrayal of Max--here, he seems like the most rounded character.

On the other hand, I think Mrs. Waverly has some inconsistencies. She seems to be extremely considerate of her children, the epitome of a maternal figure. Yet, when she hears the news of the mysterious man, she immediately starts bolting the windows. Wouldn't this frighten her children? I get the impression that she should try to assure them first and attempt to hide her panic, especially with the gullible Amelia watching.

As for Amelia, she should note something about the man sleeping or lying on the sand--it's generally uncommon, so children are almost always bound to comment on it...theoretically. Her reactions seem stifled--because you focus mainly on Mrs. Waverly's reaction, Amelia vanishes. Consider adding more description toward the end to include her.

I really like Max. He loves attention but is too prideful to clamor for it, and though outwardly he tries to be cool, he truly cares about Amelia and has a sense of maturity not to admit that the man is dead. He's layered. <3

Overall, the sentence structure is pretty repetitive. The piece could take a little more variation. The description in the beginning, "Just off the Gulf of Mexico" is too broad; it doesn't offer any accurate picture, and it simply makes me think of a map. Instead, try describing the beach or her surroundings. Is her house alone? Does she live in a city? That sort of thing.

Lastly, I'd like to point out some descriptions:

"stretched smile" -- this implies the smile is strained. The connotation (I find) is generally negative, as if she's trying to smile, not out of true happiness. A better alternative would be broad smile, wide smile, or proud smile. "Grin" would also work well.

"laughed merrily" -- I don't feel like this suits the situation. "Merrily" is too strongly positive for this sort of situation, like when someone is overwhelmingly happy.

"glared (at her son)" -- "glared" is super intense. I don't think a mother would do that to her son. This connotes hatred, not just sternness.

Hope you find this helpful.