The vine with heart-shaped leaves looks the invasive air potato vine, Dioscorea bulbifera. Check with your local Extension Master Gardeners to confirm the identification and find out about local suggestions for dealing with the plant. I'll include some links for you to do more research.
Broward county master gardeners: http://www.broward.org/Parks/Extension/UrbanHorticulture/Pages/Master-Gardener-Public-Service-Center-FAQ's.aspx
University of Florida invasive plant information: https://plants.ifas.ufl.edu/plant-directory/dioscorea-bulbifera/
Air potato in Florida from Hernando County: http://www.co.hernando.fl.us/mosquito/pdf/airpotato.pdf