The regular cage should be fine for them to recover. If there are shelves or levels, block them off if you can. Your rabbit will be more comfortable in their own cage and will probably get back to eating sooner if they feel at home.
Don't use shavings other other similar bedding as it can irritate the incision. Fleece, towels or something similar is better. If you have a litter box that has lower sides, that can be better to use or you can just take it out for a few days. Clean daily so you can monitor poops and keep the cage clean. Try to keep hay contained as well as it can irritate the incision.
Make sure you get pain medication when you bring them home. Some vets will give pre measuered syringes and others give you a bottle and a syringe and tell you how much to give. Females usually need it for a bit longer than males. Most vets give metacam.
Check the incision twice a day. It should be pretty easy to check, just pick them up carefully and take a look. It should not be red or irritated and should stay closed. Most vets use internal sutures and skin glue, so there should not be any stitches to rip out, but some rabbits might lick at it or something. A cone should not be needed and could stress a rabbit out more.
Limit activity for at least a week. Females might need more rest time. Until about 2 weeks after surgery, keep activity limited but after a week you can let them out of the cage for a little bit.
Make sure you find a rabbit savvy vet. Not all vets know much about rabbits and rabbits are different from dogs and cats. Since Duchess is 5 years, she is a bit more if a risk and you want a good vet who knows what they are doing. Diva is a bit young to be done, but should be ready in a month or 2.
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