and AnyDVD do not work correctly. It means, the only first logged in user has the access to the control application (I mean, anydvd itself). The others are not all

I found here that in 4.1.0.1:
"Fix: AnyDVD can no longer be started more than once in
multiple "Fast User switched" sessions on Windows XP."

What I have to do to get AnyDVD in other users?

You have to log off. With Fast user switching AnyDVD continues working for all users, but it stays invisible.

not really comfortable. If I would like to change settings, either I have to know the password of the first logged in user (I really don't know the password from my wife's login ) or kill the "fox" instance.

I think it would be better, if this application will control the service, not the driver directly (if i'm correct).

Any way, it's better than your competitor - DVD Region+CSS free. They were trying to install the driver under the normal user (I'm not working under the adminstrator's account) even I've installed this app before under the admin

A service would be the right solution. This is the problem - there is no AnyDVD service. Only the kernel driver (AnyDVD.sys on 2000/XP/2003 and AnyDVD.vxd on 9x/ME) and the user mode application (AnyDVD.exe).
You could ask your wife to exit AnyDVD (right click the fox - Exit) before switching users.