There is nothing else known about Mr. Ping's father other than he was the third known owner of the Noodle Shop. He had his son, Mr. Ping, take over the restaurant presumably after Mr. Ping had the "Noodle Dream".
Mr Ping's father's relationship with his father is not known, but it can be assumed that they loved each other as father and son since the noodle shop was passed down to the son (possibly after the father's death).
From what we learn of Mr Ping's relationship with his father, Mr Ping was given the ownership of the noodle shop after having the 'noodle dream'.
According to the portrait, Mr Ping's father wore a simple brown robe with light yellow trim. He also wore a noodle hat just like his son.