Kelly Rutherford -- Shows Up for Court, But WITHOUT the Kids

8:58 AM PT -- The couple's kids have arrived at court.

Kelly Rutherford defiantly showed up for the court hearing where she's supposed to surrender her children to her ex-husband -- but she did NOT bring the kids.

TMZ broke the story ... Kelly was ordered to appear before a NY judge because Daniel Giersch is demanding Kelly return their two kids to him in Monaco. Kelly's visitation period ended last week, but she's refusing to send them back to Daniel.

He insists Kelly's basically a child abductor now. The judge specified Kelly needed to bring them to court today, but it looks like she's not willing to give in ... not yet.

Giersch is not in court, but his mother is there ... hoping, we guess, to take custody of her grandchildren.