Thanks.
>> Try to login from the client, and at first, a redirect to gluu login page occurs, and i put username/password for the user i am trying to authenticate
You are getting login prompt, because there is no active session. So that's okay.
>> authentication fails and i am redirected to SP failed login page again
Please resend me the log files of this specific timing ( it's better to send that specific attempt's log ) from `idp-process.log` and `oxauth.log`.
Also record the HAR file and send that to me from this event.
>> trying to re-login from the client, no gluu login page shows, and i am redirected to SP failed login page
That makes sense, because you are trying on same window/same browser 'again' so there is already an active session. So, re-trying wont' work until and unless you hit "logout" to kill the session.