Here's an argument for your mom.
How many baby bunnies is she willing to have around?
An average doe with have 3-8 babies in a litter. And they have no heat cycle and are able to get pregnant IMMEDIATLY after giving birth.
So, babies reach sexual maturity at about 4 months. Girl gets pregnant at 5 months. First litter, lets say we'll do an average of 5 babies per litter, at 6 months. So now you'vegot 5 babies, and since dad will still be in the same cage she's now pregnant again.
So by 7 months, litter #2 comes, so now you have to take litter #1 away from mom and put them in their own cage and keep them for another month till 8 weeks old before finding them homes.
Meanwhile mom gets pregnant again, and another 5 babies on the way.
I can almost garauntee it will take a minimum of 3-4 months to find homes for the first litter of babies. So now you need two cages for boys/girls from the first litter, and a new cage for the 4week old babies to grow up in.
So you've now got three litters in three months, so 15 babies.
Now, momma is most likely going to be very sick as having babies is very hard on her, and she needs to go to the vets for an infected uterus. That's going to cost about $200 for vet visits and medicine, and the only way to save her may be to remove the uterus(spay), so that's another $100.
In the end it's cheaper to get them spayed/neutered. You don't have to buy extra cages (about 4 of them maybe more), you won't have to worry about birthing complications which means a costly trip to the vets.
There's a reason there is a saying "Breeding like rabbits".
I have a feeling she's not willing or prepared to house and feed that many rabbits.
I would also definitly try to get a hold of some shelters or rescue groups and see if any of them offer a spay/neuter program at reduced cost.
--Dawn