Hil All!
I cant solve my problem after reading a lot of sources. I have configured WebDAV IIS 7.5 site with local physical path accessing via windows authentication (enter logon/pass or smartcard with appropriate certificate) - works fine. Then I did move catalog to network source (windows network share) and got troubles with passing credentials through application user to network share. Then I tried to use basic authentication - work fine. Then I did select every kind of "Physial Path Credentials Logon Type" with same result. I need to use smartcard from external connections, I dont want to use basic authentication.
PS
Delegation on IIS computer enabled for all services to file server (where links network share). Im not sure it necessary, but it did this when publish web server through TMG.