Taxi, shuttle, or rental car. There are no ride share apps on the island, but taxis are plentiful. You can call or schedule one at your hotel. Most hotels will also offer rental cars if you want more flexibility!
From what we have gathered, this should not be an issue. Patrons come from outside the hotel to dine at restaurants. They can also congregate in the lobby and bar areas freely. The Westin will likely be more strict with pool, beach, and spa access for those staying at Playa Azul. They charge $50 for a day pass if you'd like to use these types of facilities. Michael and Holly only request that guests come do this or the all-inclusive option at The Westin on Sunday the 26th.
Michael and Holly are looking into chartering a shuttle to take people to and from the hotels, venue, and after party. Both locations have taxi stands as well, which can take people anywhere they would like to go.