As Michael Mrozek illustrates, you can run X applications that display on your wife's desktop. All you need to do is set the
DISPLAY environment variable to the right value (almost always
:0)… and get yourself authorized.
This solution requires that you have permission to read you wife's files. Access to the X server requires an authentication “cookie”, which is a password that's randomly generated when X starts and stored in a file. The file is often
~/.Xauthority; if it's not, it must be indicated in the
XAUTHORITY environment variable. Under Ubuntu with the default setup (using Gdm), your wife's session cookie is not in
~wife/.Xauthority but in a file with an automatically generated name; see ssh DISPLAY variable. See also As root can I launch a graphical program on another users desktop?, Linux: wmctrl cannot open display when session initiated via ssh+screen.
If your wife has a text terminal open, you can use
write as suggested by user7440 to write some text in her terminal. That requires that the terminal accepts such notifications; you can turn this on and off with
mesg y or
mesg n, and I don't know what the default state is on modern terminal emulators.
A more sophisticated mechanism that
talk. The talk protocol is the ancestor of chat programs; you can talk with anyone on a machine that's running a talk server and whose UDP port 517 or 518 (there are two protocol variants) isn't filtered. So install talkd , a client such as ytalk , and
ytalk wife. There's also an X client, xtalk . As far as I know, talk has simply fallen off the radar (everybody who cares uses one of the modern chat procotols), and there's no system component that would generate a KDE notification of a talk request.
While you say you can't run any IM client… would a command-line IM client running on your home machine accessed through SSH be ok? There are such, for example weechat . You'd still be depending on the some server to connect you with your wife, but it would only be accessed from your home machine, not from your phone.