Video Continuity mistake: When the army soldiers are yelling into the baby monitor that the kids are heading up to Andy's room, the baby monitor is right in front of Woody on the floor. Yet, when the camera pans out to show all the toys scrambling for their places the monitor is gone, and Hamm is right in front of Woody. Then, when the camera zooms back in to show Woody, the baby monitor has reappeared. (00:12:30)
Continuity mistake: Near the start, when Woody mentions the party being moved to today, there are 2 black spots on the wheel by the toy box that change place. Note the spoke of the wheel.
Answer: This is a Disney/Pixar production, at no point are they intimating that kind of a relationship between son and father. If anything, the father simply doesn't care what his son gets up to so long as he isn't disturbed by it. Any other inferences you get from the movie are for you to contend with, but the family nature of the movie would suggest beating/abuse is not the answer.
GalahadFairlight