If you want to convince your parents to keep her inside I would watch and show them Lennon The Bunny's videos on YouTube. She has some very informative videos that may show them how you can keep her inside. You could put up some baby gates or keep her in a spare bedroom, or in your own room.
What a lot of people with dogs do is keep them in a pen that other pets can't get into, and keep them dog in a separate part of the house (or on a walk) when free-roaming. Just be sure she has a least four hours of exercise outside of a pen a day.
Free roaming indoors is very inexpensive (more so than having in a hutch. Hutches and cages can be expensive and take time to build. All you need for free roaming is a playpen, usually about $20-30, and some bunny proofing supplies, which is about $40. And, your rabbits health and quality of life will be much better.
All you would have to do is bunny proof the house (at least the area she would be), and keep her away for your doggo. An easy set up to keep her in when not free roaming would be something like this:
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It's super cute, and would keep your dog out.
It would take some more time and money to build, but certainly no more than a hutch or cage.
An easier set up could look something like this:
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You may want to start with something like this since it would be more inexpensive and your parents would probably be less opposed to this for that reason. If you wanted, after your parents see how great having a more free ranged - indoor rabbit is you could make something like the above picture.
Just an idea to consider