Looks like Digicel has changed their website a bit and no longer features their mifi device on there, but basically what you will most likely want to get from them is something similar to this: http://www.amazon.com/Huawei-E5331s-2-Mobile-Hotspot-T-Mobile/dp/B00871NPP6

It is called a "Mifi" device and will provide wifi for up to either 5 or 10 different devices at once. Based on what you said above, this is likely what would be most useful to you. I am assuming that they still sell these, but you might call the Road Town store to confirm.

I can't imagine it wouldn't work on JVD, here is the coverage map: http://www.digicelgroup.com/vg/en/mobile/plans/coverage-map.html

Basically, as long as you have line of site to a cell tower, you should be good. And the cell towers are all over the place now.

As long as there is not a long line at the store, you should be in and out in 30 minutes or less.