Playing piano by ear does not need to be difficult. Start with your basic chord structures and go from there. Rhythmic patterns are the answer to freedom to play be ear on the piano.
I just posted a youtube video for Love Me Tender. This has a fabulous rhythmic pattern that can be used in many 4/4 time signatures. Check it out here http://www.youtube.com/watch?v=IR75erMsSvM&list=UULXd_oaGk_U_pfwkvvxH2kA&index=1&feature=plcp
You do not always need to know the notes in the right hand to play a song. Once you know the chord structure and are able to freely sing or hum along, then you will see that the melody notes are intertwined among the chords. That’s when you start to break down the chords and involve the melody line. Use the notes within the chord structure to color your melody notes.
Fingering can be tricky, but there is no right or wrong way. Do what is easy for you at the time and go from there. Repeat, repeat, repeat.
Then, at the next family gathering when it’s time to have the sing-a-long, you will be much better prepared. You will no longer need to sight-read those notes. Instead you will be looking at the chords and everyone will be singing along. That’s the path to great playing piano by ear!