Bobby Brown's Family Shooting Reality Show During Bobbi Kristina Crisis

Bobby Brown's family is grieving over the dire circumstances surrounding Bobbi Kristina ... and we've learned they're also shooting a reality show.

Sources connected with the production tell TMZ ... Bobby's 2 sisters, brother and their kids are shooting the show about their lives, and part of it will chronicle Bobbi Kristina fighting for her life.

Bobby's lawyer tells TMZ his client will NOT appear on the show.

Bobby's sisters have a history. Leolah is the one who went on the record blaming Ray J for Whitney Houston's death, claiming he fatally fueled her cocaine habit.

Tina is the one who did a sit-down interview and claimed she did crack with Whitney. Tina and Shayne are also the ones who fought at a hotel near the hospital. She hit her son Shayne with a bottle. It's unclear if that will be on the show.

It appears that they have not shot video in the hospital, but we're told they have regular debriefs at home on camera where they talk about the tragedy.