Is it against the rules to block a robot from entering its home zone at the end of the game? And if it is allowed, do we or the other alliance get penalized for being pushed into the opposing home zone? Thnx 
If you block a robot from its home zone without entering its home zone, that’s just good defense. If you’re pushed into the home zone and there’s no way you could avoid it, there’s no penalty on you. If you enter the opposing home zone without being acted upon by an outside force, there will be a penalty assigned.
These two rules should address your question:
<G24>
[LEFT]Clearing HOME ZONE – the first audio signal, sounded five seconds before the start of the END GAME, serves as a warning for ROBOTS to exit from the opposing HOME ZONE. ROBOTS attempting to exit from the HOME ZONE after the audio signal may not be blocked or impeded in this attempt.
<G25> END GAME play – ROBOTS may not occupy the opponents HOME ZONE during the END GAME. Any ROBOT in an opponent’s HOME ZONE at the start of the END GAME will be assessed a 10-point penalty. A second 10-point penalty will be assessed if the ROBOT is still in the HOME ZONE 5 seconds after the start of the END GAME. Another 10-point penalty will be assessed if the ROBOT remains in the HOME ZONE 10 seconds after the start of the END GAME. However, a ROBOT that has been blocked or otherwise prevented from exiting the HOME ZONE (as described in Rule <G24>) will not be assessed any penalty.
[/LEFT]