Whitney Houston's daughter engaged in some hardcore PDA  -- including a kiss -- with her secret BF yesterday ... a guy who happens to be her pseudo-adopted brother ... and TMZ has the video.

19-year-old Bobbi Kristina was seen in a full-on lip-lock with 22-year-old Nick Gordon during a lunch run in Atlanta Tuesday ... confirming suspicions the two are romantically involved.

As we previously reported, Nick and Bobbi go way back ... when Whitney unofficially "adopted" Nick into the family roughly 10 years ago after learning Nick was having problems at home. He's been living with the Houstons ever since.

Again, Bobbi and Nick share no blood relation ... but we still gotta ask ...