Welcome AFbrat! Wendy has give you some great advice! The House Rabbit Society's site really is a great resource! I also agree that volunteering is a great way to get experience and really see if you want a rabbit. It's also something BOTH you and your mom could do together.
The fact that this rabbit would also be your mom's is great. It's better to have an adult share in the love and responsibility. Since rabbits can live to be 10 - 12 years, many times that means you kids turn into highschool students with tons of responsibilities and actives or even off to college.
Rabbits are not easy pets, and though most can be litter trained, some don't always take to it right away, so depending on the rabbit, it can take time. You just have to limit freedom at first. You don't want to let him roam free right away. Sometimes if a bunny gets too much freedom too fast, is when poor litterbox habits sink it, and it can make it more difficult during the training process.
I think the best bet you would have is to find a local rescue (whether you volunteer there or not) and talk to them about their bunny's personalities and if some bunnies already show good litterbox habits. (many times they do!) . Plus, most rescue groups already have rabbits that are spayed and neutered. That is really important in regards to litterbox habits.
Also, note: Baby bunnies are cute, but they are a mess! Older bunnies are easier to litter train.
Some of the things that can go wrong are destruction of wires, carpet, furniture. So you really have to house proof your place. Check out the House Proofing section in the Bunny Info Page.
I have three bunnies. Two of which do not chew or cause any damage. But one, he's a disaster if I don't use wire protectors, and put phone books, boxes, and other chews as distractions. The moment he gets bored, he's ready to start on the carpet. He has melllowed with age, but I still have to watch him now and then.
The other "thing that can go wrong" is that vet bills for rabbits are not cheap. Many times people are not aware how expensive a vet visit can be - especially if it's an emergency. Rabbitsare actually considered "exotic" in the vet world - meaning they need a special kind of care - that can run the vet bills up.
There is pet insurance that can help with the bills though for around 12 bucks a month.
I think you are one smart cookie to learn more so you can bring any valid arguement to your dad. Plus it'll show you've done your research. After you've fully looked into it, you may even say you would rather not make a commitment to a rabbit, maybe something else. But if after you and your mom have researched and you both still want a bunny companion, at least you'll be prepared, more prepared then many of us who got our first bunny companion. So you're father should be proud of you.
I know you said your father put his foot down. What are his biggest concerns about having a house rabbit? What is he picturing in his mind? List those, and then address each one. And if there are negatives, don't sugar coat the answer with only positives. It might be best to say you understand how that could be a problem or how he would be concerned with that, and your research regarding that shows....... and then say what you will do to try and prevent that "negative" from happening.
If you want help with that - just post the "Dad Concerns" list here, and I'm sure we can all pipe in with our experience and advice for each subject.