Nginx reverse proxy root URI issue - nginx

Question

I have an application running in Kubernetes with the following topology:
Some-ingress-controller--> nginx reverse proxy -->dynamically generated services.
I have set the NGINX reverse proxy with the following test configuration
location /mysite1/ {
proxy_set_header Host $host;
proxy_set_header Referer $http_referer;
proxy_set_header X-Real-IP $remote_addr;
proxy_set_header X-Forwarded-Proto http;
proxy_set_header X-Forwarded-For $remote_addr;
proxy_set_header X-Forwarded-Host $remote_addr;
proxy_pass http://myservice1.default.svc:9000/;
}
So far everything works fine - when I go to my website http://example.com/mysite1/ I see what I expect from the myservice1 application hosted at http://myservice1.default.svc:9000/. However, the application myservice1 issues requests to various internal (internal meaning they are part of the same container) resources on /get_resourceX. When the myservice1 application tries to access these resources they will be accessed at http://example.com/get_resourceX/ and not at http://example.com/mysite1/get_resourceX as they should - and that is my problem.
What could work is to simply reverse proxy all the relevant resource names as well. However, then I would need to do the same for http://example.com/mysite2, http://example.com/mysite3 etc. which is impractical since these are generated dynamically.
Another possible solution is to check the http Referrer header and see whether it originates from mysite1 - but that seems awfully hackish.
How can I easily have myservice1 requests issued to /get_resourceX served by itself? Is there a generic way to set the root path for the myservice1 application to myservice1?