I rented a movie on my iPad but there isn't enough space on it to download the movie so now I'm trying to either watch it on my AppleTV or laptop through iTunes, but I can't seem to find how to do that. Is it not possible?
No, it is not possible.
See this Apple Support Document for more information:
Movies rented on iPad cannot be transferred to other devices and can only be viewed on iPad.
You'll have to expand the section on "Movie rentals on iPad" to see the above quote.
Your only option is to free up enough space to watch it on your iPad.
I have an Apple dock cable with an HDMI connector. Using that cable I was able to play the movie
That is a disgrace. My parents bought an Apple TV on the promise of compatibility between Apple devices, and yet now they find that for some bizarre reason the rules are different for their iPad. They rented a film on iTunes on the iPad whilst they were out of the house, and found that it could only be watched on the iPad, unlike films rented on their MacBook which can be watched on all devices. There was no warning or disclaimer about this, only a bit of small print on the we page linked to. I think that is a con.
if you have an apple tv all you have to do is stream a movie from your iPad or other apple device. No problem
We're looking for long answers that provide some explanation and context. Don't just give a one-line answer; explain why your answer is right, ideally with citations. Answers that don't include explanations may be removed.