I also got stuck on the second level chasing dad after the wizard and squirrel go to the bar.
I had also managed to beat dad to the exit in the previous level, so after reading this comment I tried to reproduce the glitch to beat dad to the end but was unsuccessful.
Based off the theory of beating dad the first time causing the glitch in the second level, I tried to go back and finish the first level without beating dad, but it wouldn't accept the level as passed.
I then started a new game for a fresh start, but am similarly unable to pass the first level - I believe that this inability to win after dad was the reason I thought I needed to beat dad to the exit in the first place, but it doesn't seem possible to do so in the second level.
I've included a screenshot of the second level with my character at the exit. I can provide more if necessary.