It's really important that female bunnies are neutered, due to the high rates of uterine cancer in unspayed girl buns. I would show your mum some info on the importance of spaying, and perhaps you could come to an agreement to do some extra chores or something to pay her back over time if you really want to keep the bunny. A good starting point is the HRS http://rabbit.org/faq-spaying-and-neutering/
If spaying is something your mum refuses to do, then it might be best to rehome her, as it will be hard to litter train her when she's not fixed, making the other issues - such as letting her out for runs, also difficult I imagine.
SO, if you were rehoming her I would -
a. do some research and find a no kill shelter that has experience with rabbits, or a specialised rabbit shelter, even if it's further away
b. If you're rehoming her through a site like craigslist, you could try selling her for the price of a spay, and hand her over at a vet once they've paid for the treatment. Or, you could ask for a donation to an animal charity that is large enough to put off people who are just looking for snake food. You can also ask the new owner questions, and give them a 'cheat sheet' with information about proper diet, cage size, signs of illness etc.