The only beach that seems to fit your needs here is Barbados ... it faces south, and is the only one that does so. Martinique faces west (as Catbertdave showed you), which explains why it had full sun in late afternoon. Trinidad South's beach faces west just like Martinique's does, but Trinidad South will be comprised of pirate rooms which will cost more per night, and since you said you won't spend the extra $ on preferred location I doubt you'll decide to spend extra $ on a themed room. And Trinidad North's beach faces pretty much west, but again, it's a preferred location village.
So the only thing you have left is Barbados.
As for where "they" draw the line ... it's really up to you. The prohibition against swimming isn't for preventing drowning as much as it is for preventing illness. There are microbes in the water in most lakes that can make you sick. It's OK to get your feet wet, but you don't want to expose your kids' mucous membranes (eyes, nose mouth) exposed to that nasty water. It's very unlikely they'd have ANY ill-effects from simple wading up to their ankles or even a little further, but kids will be kids, and if they splash a lot or they rough-house and fall into the water, then you're inviting trouble.
... we laughed about whether it might be animatronic! Didn't know Florida had armadillos...thought it was a Texas thing! In any case..don't swim in the water! Perhaps you could fill a few empty drinking water bottles from your room so the kids can make wet sand for sandcastles.
