your area is completely without birds of prey? that’s surprising. and you can’t count on predators behaving around prey. your dog is also a predator. he may be trained to leave the rabbit alone, but that doesn’t mean you should leave them together unsupervised.
is your rabbit not used to being handled? are you rough when putting him in the cage?
A hematoma doesn’t necessarily have to cost hundreds of dollars … talk to your vet about payment options or care credit … or ask your vet if there are local animal welfare organizations that may be able to help.
There are no “home remedies” that I am aware of.