Tyrese Gibson -- Paul Walker Dragged Into Nasty Custody Battle

Tyrese Gibson claims his baby mama is using Paul Walker's death to shame him in their child custody war ... TMZ has learned.

Norma Gibson filed court docs claiming Tyrese is a bad dad, who should have stayed in L.A. to spend time with their 6-year-old daughter after Paul Walker's death ... because he had time on his hands since "Fast & Furious 7" was put on hold.

Norma says Tyrese blew off his little girl, choosing instead to go "gallivanting throughout Dubai ... staying in expensive hotels ... partying on yachts, sky-diving with other movie stars, driving expensive cars, and making special appearances in night clubs."

But sources close to Tyrese say he's indignant Norma is using Paul ... and he went to Dubai on business. He had 4 gigs and he needed the money -- ironically to pay the child support Norma was demanding.