Rihanna Was at Home With Her 3 Kids During Shooting: Source

Rihanna was home with her 3 kids at the time an assailant targeted their L.A.-area mansion with gunfire -- A$AP Rocky, the father of the kids, was also home.

Sources with direct knowledge tell us ... the singer was shacked up inside her house with the children she shares with A$AP -- namely RZA, Riot Rose, and Rocki Irish -- before all hell broke loose on Sunday afternoon.

The suspected shooter, Ivanna Lisette Ortiz, allegedly fired off several shots from her vehicle at the residence ... but luckily RiRi and her youngsters were not injured, our sources said.

The Los Angeles Police Department responded to a call of "shots fired" and spoke with the person who reported the shooting to get a description of the suspect. Officers quickly found the alleged shooter nearby and placed Ortiz under arrest. Police said a weapon was recovered.

Ortiz was booked into the L.A. County jail for attempted murder, and bail was set at a whopping $10,225,000 ... which she has not posted.

Weeks before the shooting, on February 23, Ortiz allegedly posted a strange Facebook message about Rihanna, writing ... "@badgalriri Are you there? Cause I was waiting for your AIDS 5-head self to say something to me directly instead of sneaking around like you talking to me where I'm not at."