Any time you change the context path in the proxy (/ -> proj1) you create a whole heap of problems to solve. Your immediate cookie problem can be solved with the ProxyPassReverseCookiePath directive. I then suspect you'll find the next problem to solve. You'd be better off redeploying your application as the ROOT web application so that your ProxyPass directive is ProxyPass / https://realdomain.tld:8443/
As an aside, it looks like you are proxying to Tomcat's https connector. If you aren't careful you will create security problems for yourself if httpd receives requests over http, proxies them to Tomcat over https and Tomcat treats those requests as being received over a secure channel.