HAProxy – How to Read the HAProxy Stats Page

That is not correct. There would be a stats page on http://yoursite.com:1935/haproxy?stats

To overcome this add another listener-

listen stats :1936
    mode http
    stats enable
    stats hide-version
    stats realm Haproxy\ Statistics
    stats uri /
    stats auth Username:Password

Then go to http://yoursite.com:1936/ and login.

Make sure your firewall isn't blocking this request.

What you're looking for is "sticky sessions", and you can use appsession parameter in HAProxy to enable that:

appsession <cookie> len <length> timeout <holdtime> 
           [request-learn] [prefix] [mode <path-parameters|query-string>]

When an application cookie is defined in a backend, HAProxy will check when the server sets such a cookie, and will store its value in a table, and associate it with the server's identifier. Up to characters from the value will be retained. On each connection, haproxy will look for this cookie both in the "Cookie:" headers, and as a URL parameter (depending on the mode used). If a known value is found, the client will be directed to the server associated with this value. Otherwise, the load balancing algorithm is applied. Cookies are automatically removed from memory when they have been unused for a duration longer than .

The definition of an application cookie is limited to one per backend.

Example : appsession JSESSIONID len 52 timeout 3h

Refer to HAProxy documentation for more details.