First of all, be absolutely calm. Second, be absolutely certain that you are right- set in stone, as it were. This sort of "parent"* exists at just about every level. To be honest, do not expect a great deal of improvement at the conference. If somebody is into "taking people outside" then there is not a great likelihood of reasoned discourse taking place. Recognizing that, you still have to make the attempt. Be reasonable, but in this case, don't yield unless your administrator backs out (then you are pretty much out on a limb). Appeasement only makes this sort of "parent" worse.
Aside from that- go in prepared, with all necessary information, copies, etc. handy.
*Note- this term is only biologically correct. Many have children; far less are actually parents.