The short answer is yes, spouses have rights under the Jones Act. You don't have a separate case, but you do have rights if your spouse's injury or death has negatively affected your family. Many lawyers won't bother with adding your spousal claim to the Jones Act lawsuit, so you need to hire a Jones Act attorney who specializes in reviewing how your spouse's injury or death affects the whole family.
Brian had a client who injured his back on a barge who was trying to decide if he wanted to hire us or another firm. The client was financially in a lot of trouble, and the other lawyer offered him a lot of money on the front end of his case so he picked the other lawyer. The mariner had back surgery and massive bills that put a huge financial strain on his entire family, but the lawyer settled his case for peanuts. Brian was outraged when he found out how low the mariner's case had settled for, and this mariner's story serves as a reminder to be very careful who you hire for your case.