I'm pretty sure those are true feelings for his real father and the intensity of the scene was unplanned. The hug his uncle is giving him is true comfort.
It wasn't meant it be funny. Actually, the line "why don't he want me man?" Was an adlib- will smith was talking about his real dad in real life and they were crying for real.
http://www.projectcasting.com/news/the-real-story-behind-the-most-heartbreaking-scene-in-the-fresh-prince-of-bel-air/
I have some sad news for you