current way to show pop-up windows in other users sessions?

[M. Fioretti]

Greetings,

it's been a looong, long time since the last time I did this, so I
need a bit of help to refresh my memory. In a sense, what I'm unable
to remember right now is what docs I should read...

I have a cron shell script that, if some event happens, must:

1) check if a *local* user A is currently logged in, and in which
   session/display

2) if yes, pop up a window in the session of user A, showing the
   content of a text file

I know how to do (1) with "who":

[marco at polaris ~]$ who
bill    :2           2013-09-10 19:56

this tells me that "bill" (i.e. NOT me, another user!!!) **is**
currently logged in on display :0

and I also know how to do (2) with kdialog, zenity, xmessage...

but of course, if I launch kdialog I get nothing but the "Error: can't
open display" message. Setting DISPLAY to ":2", "ip.address:2",
":2.0"... doesn't change anything.

(many) years ago this was solved with xhost +, but not now. So, what
is the current way to make (2) happen? Possibly one that is
distribution-agnostic?

TIA,
	Marco