How do you cope when your family doesn't understand your bond with your rabbit?

I'm feeling completely overwhelmed and could really use some advice from other rabbit owners.
A little over a year ago, I adopted my rabbit, and from that day I made a commitment to give him the best care l possibly could. He's become part of my family, and we're incredibly bonded.
This week I was supposed to fly home for my cousin's wedding. My parents kindly paid for my flights and for my rabbit's boarding because money has been tight.
A few days before my flight, my rabbit suddenly developed GI stasis and had to be hospitalized. The vets now think it's most likely an infection. Thankfully he's improving, he's eating again, his gut is moving again, and he's slowly getting better but he's still recovering.
Both the vets and the boarding owner strongly recommended that he recover at home instead of going into boarding, especially while he's still healing and on medication. So I cancelled my trip.
The hardest part has been my family's reaction. My parents don't really see animals as family, and my dad told me he couldn't understand how I could choose a rabbit over them. That really hurt, because to me it isn't about choosing one over the other. If my rabbit hadn't become sick, I would have been at the wedding without hesitation.
This is simply the responsibility I accepted when I adopted him, and I can't let him when he is sick....we needs each others.
I feel guilty about missing such an important family event, and at the same time I'm already terrified and worried about my rabbit.
For those of you who have been in similar situations, how do you cope with the guilt, the stress, and people who don't understand the bond you have with your rabbit?