2:39 PM PT -- Heather has since filed her own emergency petition for custody ... in it, she asks the judge demand Nick submit to drug testing. She also claims Nick hosts a variety of high stakes poker games at his home with strangers coming and going, making it unsafe for their daughter.

Finally ... Heather mentions a photo Nick posted on his Instagram account in which she claims cocaine can be seen on a table next to one of his friends -- another sign his home is a dangerous environment.

A judge has not yet ruled on Heather's petition.

Nick Cassavetes was just denied an emergency custody petition he'd requested in hopes of getting his daughter back.

A judge in Oklahoma ruled Friday that there was insufficient evidence to justify Nick's daughter was in danger ... and therefore no reason to grant Nick his emergency petition for custody.

TMZ broke the story ... "The Notebook" director claims his estranged wife, Heather Wahlquist, is hiding their 13-year-old daughter, Barbie, from him ... and they've been on the run for the last month.

Cassavetes has filed a crime report claiming Heather is violating their custody arrangement and has effectively stolen Barbie from him.

TMZ broke the story ... Heather claims Nick is only doing this as a form of revenge for leaving him 5 years ago.