I often get errors like this when running Vagrant:
VBoxManage: error: A NAT rule of this name already exists
VBoxManage: error: Details: code NS_ERROR_INVALID_AR
I came here with the same problem; with your hint about deleting the rule I found that you can use the VirtualBox GUI to find the rules and delete them.
Of course, this only works when you are working on a machine with a GUI desktop.
Network
from the list on the left and open the Port Forwarding
dialogueFrom here you'll be able to directly remove the rules.
http://i.stack.imgur.com/6fQQc.png
Looking at the rules, it seems they just get a name that is equal to the port being set. So you can also look at the Vagrantfile, and search for a line like this:
db.vm.network :forwarded_port, guest: 5432, host: 5432
And guess that the name of the rule will be 5432
. The name of the rule for forwarding the ssh port 22, is called ssh
$ vboxmanage modifyvm "vbox-id" --natpf1 delete "5432"