Heather Mills -- No Leg to Stand On ... In Court

Heather Mills got shut down by a judge, who turned down her request to delay a settlement meeting over a lawsuit ... so she could ski her heart out in Aspen.

Heather was required to show up for a mediation by the end of March, but she filed papers on March 20 asking for permission to delay the hearing because she was training for the 2014 Paralympics -- in Aspen, of course.

Heather is being sued by her former publicist ... who claims she was a nightmare who made false allegations that Paul McCartney was a drug-abusing wife-beater. The publicity company also claims it got Heather a shot at being on "Celebrity Apprentice" but she would only agree if Trump would rig the competition so she would win -- Trump scoffed at her. And the publicists say Heather stiffed them on the bill.