I was interested in using docker and had two question, is there a way to keep two different dockers from conflicting?

I have a conflict between NGINX and Vaultier.

Also is there a GUI management tool for Docker?

Docker containers are isolated and won't conflict with each other. You might be trying to expose both containers to the same port on the host?

You could supply some more detailed information for others to be able to help you identify your issue you know.

afaik there isn't a GUI management for docker (yet)

I hae a machine that has NGINX installed and running listening to port 80. I have a docker file (however to put that) with a process in there that will also try to listen on port 80 (apache). By running this docker file should I expect any conflicts?

Each docker instance (by the dockerfile) is run isolated from the host so it should be able to claim port 80 itself. it will have to be 'exposed' by docker to the physical world for the port to be available. that expose can not be the same port on the host...
eg.. on my physical host, hosting docker infrastructure, I have an apache server running on port 80. in docker container 1 I have nginx, also on port 80, and on a second Docker container I have lighttpd, again, on port 80.

Only the physical host will be accessible from outside, unless you 'expose' the ports of the containers to the outer world.. Docker can be set to expose container1 port 80 to physical port 81 for the nginx, and container2 port 80 to physical port 82 for lighttpd.