Chyna was in L.A. with her nanny, who's clutching the 10-month old, as she spent time with the kid.

TMZ broke the story ... Chyna and Rob have 50/50 joint custody and he's paying her $20k a month in child support. Don't be surprised if Rob goes back into court to either reduce the support payment or eliminate it, because we've learned he's broke and his family is paying the $20k.

Chyna will join Amber Rose today for the annual SlutWalk. Chyna will appear with her lawyer, Lisa Bloom, and top of mind for them is the revenge porn Rob posted in anger.