nginx as a reverse proxy - nginx

Question

I'm trying to use nginx as a reverse proxy to a couple of web applications deployed within docker containers. I can only expose port 80 from the docker server, and want to allow access to shipyard and rabbitMQ management web app.
Ideally, users could access the services via:
http[:]//10.10.10.1/shipyard/
http[:]//10.10.10.1/rabbitmq/
After quite a bit of research, trial and error this is my nginx config:
upstream rabbitmq {
server 127.0.0.1:8888;
}
upstream shipyard {
server 127.0.0.1:8080;
}
server {
listen 80;
server_name 10.10.10.1;
location /rabbitmq/ {
proxy_http_version 1.1;
proxy_set_header X-Forwarded-Host $host;
proxy_set_header X-Forwarded-Server $host;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header Upgrade $http_upgrade;
proxy_set_header Connection 'upgrade';
proxy_set_header Host $host;
proxy_cache_bypass $http_upgrade;
proxy_pass http://rabbitmq/;
proxy_redirect default;
}
location /shipyard/ {
proxy_http_version 1.1;
proxy_set_header X-Forwarded-Host $host;
proxy_set_header X-Forwarded-Server $host;
proxy_set_header X-Forwarded-For $proxy_add_x_forwarded_for;
proxy_set_header Upgrade $http_upgrade;
proxy_set_header Connection 'upgrade';
proxy_set_header Host $host;
proxy_cache_bypass $http_upgrade;
proxy_pass http://shipyard/;
proxy_redirect default;
}
}
When I access either path the apps I run into a couple of problems, which I believe maybe related:
shipyard:
Tries to load files from http[:]//10.10.10.1/api/containers, when it should be http[:]//10.10.10.1/shipyard/api/containers
rabbitmq:
Everything appears to work, until the server attempts to make a restful call:
+++ PUT: http[:]//10.10.10.1/rabbitmq/api/queues///test2
The server response with 405 (Not Allowed). At first I thought the /// was the problem, that is how the rabbitMQ management application works.