Just copy the html source for the search box into the pages where
you want it and change the ACTION url to be fully qualified.
The altavista clone form looks something like:
<FORM METHOD=post ACTION=/texis/webinator/av>
<INPUT NAME=query SIZE=55 VALUE="">
<INPUT TYPE=submit VALUE="Submit">
</FORM>
Change it to:
<FORM METHOD=post ACTION=http://A/texis/webinator/av>
<INPUT NAME=query SIZE=55 VALUE="">
<INPUT TYPE=submit VALUE="Submit">
</FORM>
Where "A" is the hostname of machine A you refer to below.