Showing up nude in public where there also happens to be warm water, a good breeze, and naked females romping about is going to make your son’s arousal significantly more likely. I suggest that you refrain from insisting to your wife that erections do not happen at nudist places, especially among adolescents, because that statement is way off the mark.
You commented that you didn’t mention anything to your wife about beach chubby in the water (“I never told my wife.”) The lad is very likely able to sense your requirement for secrecy in this issue and that fact alone will make him uneasy about it, or even ashamed.
The following time he gets an erection in your presence, be casual about it.
Tell him it is part of life, there is nothing wrong with having one, he is a completely normal boy and there’s no need to be embarassed. But do underscore the necessity to act appropriately if (when) it occurs around others, by not waving it about like a big flag and to only ignore it if he can not readily hide it. Not bringing others’ focus to it’s the top plan of action. If someone does notice, he should remain cool as if nothing is going on.
And as one poster already suggested, make sure that your daughter does not make fun of him if (when) she sees him with an erection. Thirteen year old boys may be very sensitive about those remarks.
I also propose having a discussion with “the wife” and admit the information you gave her is not completely correct. She’s going to http://wnude.com/nudist-teens.html see your son with an erection one day at the resort. She has to understand he is having them, and supplying right info on the issue will decrease her shock and embarassment. If your wife understands how likely and normal erections are for a young teen boy, she can take it in stride when it does occur and not make your son feel awful about an uncontrollable body function.