I'm not going to lie, this is a tough subject to break to them! coming from me, a teenager who started my own rabbitry in September 2019!!
I actually have some advice for you, not so much your parents. if you currently own a rabbit, then you clearly know the responsibility and amount of work that a rabbit is. now imagine 10x that. baby bunnies are a LOT of work, and owning a rabbitry can be quite emotional. you have to be prepared for losing baby rabbits unexpectedly, valuable mothers dying in labor, and many other health problems. with school (and afternoon part-time job if you're like me) it can be a lot to balance. Rabbits need constant attention, and I'll be the first to admit I couldn't do it without my parents. my mom still helps check in on the babies and make sure they all have food / water when I'm at school. so keep that in mind - are your parents animal people? I feel like the bad does balance out with the good, but it still can be very stressful and emotional at times.
after much time and research, this is the way I started my rabbitry and I hope that you will consider doing the same. Don't go straight in and buy multiple does and a stud or two. I recommend getting one doe to start, and borrow a stud from a local breeder. expect to pay a fee of around $20 to $40 for the breeding or the breeding in exchange for pick of the litter. I recommend paying them a fee over a baby bunny because babies tend to be a lot more valuable than $50. at least for me - with purebred holland lops, I get around $200 to $300 dollars each, with the occasional $350. this is not always the case, especially if the bunnies are not in demand or not pedigreed. as mentioned earlier, always have a backup plan on what to do if your baby bunnies do not sell. mine is to reach out to people I've seen on craigslist who are wanting a special needs baby bunny, and give for free if it has special needs / something wrong and this person is willing to give it a good home. if a rabbit has seriously something wrong, the humane society can always help but be prepared for them to take it away once three+ months old, and for you to never hear about them again unfortunately. my most common method, is to use my empty cage that I have designated for baby rabbits. sometimes mom needs a break, so once the babies are over 8/9 weeks that's where they go. thankfully, my rabbits have been in high demand so far, and I have never had any NOT reserved by the time they're meant to go home.
anyways, my most valuable advice is to always go with PEDIGREED stock, quality over quantity, and start small. be prepared to invest into quality proven (had successful litters in the past) does / bucks that are somewhere in age of 10 months, to 3 years - preferably no older than that, as they tend to slow down at around 4 years. you should start with a big budget on buying stock, around $250 to $300 per rabbit. I got lucky starting out my rabbitry, doing a "borrow out" with a local rabbitry's doe. if you're not familiar with this, basically you pay them a flat fee of $100-$200 and a returnable deposit of what the rabbit is worth (i.e. $250) That is returned upon the doe in good health condition. this deposit includes stud service and the backup one if she didn't take on her first litter, and constant support from the breeder on any questions you may have.
hopefully this helps! I wish I could go back in time until my younger self all of this, but since I can't the best I can do is help you ☺ if you have any questions, or are confused of any of this, please reach out to me and privately message me! I would love to help, and see updates of your babies once you decide to start a rabbitry in the fall!