Well we call it tiucu (tuishou, push hands), but it is certainly not taiji push hands. It can be as hard or soft as you like, but it should be more a conversation then a contest. My teacher has told me not to be sleepy when I do it, so maybe I am a bit too relaxed.
As far as I know there are no jalan panjang (long movements) done as two person exercises, but all the jalan pendek (short movements) can be done that way. There are also many two person exercises that practice the components of tuicu, but they are not set forms, rather they are more back and forth practice in simple movements like block and punch, or applications like ambilan (sweeping, throwing).
Josh
PS. Yes it is bangau putih. Your relative is lucky to see the head of our school. He has skills that go beyond my understanding.