You are distressed that the bunny does not like to be held. Consider for a moment, however, the natural history of the rabbit. This is a ground-dwelling animal that is a prey item for many predators. It is completely against the nature of the rabbit to be held far above the ground where it cannot control its own motions and activities. When you force her to be held against her will, you reinforce her instinctive notion that you are a predator who is trying to restrain her. Holding her while she struggles and kicks is not only dangerous for you and the children (You may have noticed her sharp claws by now!), but also for the rabbit. I wish I didn't know how many young rabbits come into our vet's office with broken legs, necks and spines because people insisted on carrying them around and handling them against their will. If you love your bunny, you won't do this.
Think about it: if your dog or cat didn't like to be carried around, you probably would not force the issue. Why treat your bunny any differently, simply because of her superficially "toylike" appearance? To understand rabbit behavior, you have to begin to think like a rabbit!
First, buy yourself a copy of The House Rabbit Handbook by Marinell Harriman. It's the most accurate book about rabbits available today.
Second, remember that a rabbit, unlike a dog or cat, evolved as a prey species. Dogs and cats are predators, and most do not have a natural fear of being held. Reinforcing this natural tendency, breeders have selected generation upon generation of domestic dogs and cats so that their descendants have a short "flight distance". This means that domestic dogs and cats are generally not afraid of humans.
Domestic rabbits are very different in this respect. For centuries, rabbits have been bred primarily for meat, fur and physical characteristics. That means that when you adopt a rabbit, you adopt a beautiful animal with domesticated physical features--and the heart and spirit of a wild animal. It is much more challenging to win the trust of this kind of sensitive, intelligent creature than it is to win the heart of a puppy or kitten, who has been bred to trust you from birth.
Most rabbits are naturally shy. It is up to you, the flexible human, to compromise and alter your behavior so that the bunny understands that you are a friend.
Following are a few steps you can take to win your shy rabbit's trust.
1. You and bunny should be together in a private, quiet room. No other pets. No distractions.
2. Have a little treat, such as a carrot or a tiny piece of apple, banana or a little pinch of oats in your hand. (These foods are only for small treats! Rabbits fed a diet with too much digestible carbohydrate are excellent candidates for serious gastrointestinal disorders!)
3. Lie on your tummy on the floor and let the bunny out of his "safe haven" (hutch). It's quite crucial that this hutch have a door that is accessible to the rabbit so that you don't have to lift him when you take him out or put him back in. The bunny should have absolute freedom to choose when he comes out. Don't force the issue. The bunny's natural curiosity will bring him to you.
4. Don't expect your bunny to approach you right away. Remain quiet and patient, even if it takes an hour or more. Rabbits are naturally curious, and eventually, he will come over to sniff you.
5. Resist the temptation to reach out and pat the bunny. Instead, let him sniff you, hop on you and just get to know your smell. This will teach him that you are not a threat.
6. If the bunny finds the treat you have, hold it while he nibbles.
7. Do this every day. Gradually, you can start to touch the bunny by giving him a gentle "scritch" on the forehead (bunnies love this!). Never force anything, and never chase the bunny. This will only undo all the patient sitting you have done to gain his trust. A rabbit does not generally like to play "chase" with an animal that is thirty times his size. It is simply not natural behavior for him, and it is not a sign of low intelligence!
8. As the bunny gradually becomes less shy, you can become more familiar with him, stroking his back, letting him lie with his side pressed against your arm...whatever feels comfortable and natural to both of you. Many rabbits seem to find a face less threatening than a hand. Your bunny may gladly allow you to give him a warm "nose nuzzle" (especially if you hum very low and soft; this is the way rabbits sometimes communicate among themselves), even if he won't let your hand come close.
9. Once the bunny learns that you are a friend, he will bond very strongly to you. It's important to have him neutered (or her spayed, if it's a girl) once s/he reaches sexual maturity, because otherwise s/he'll want to make love to everything, including you--whatever appendages happen to be within reach. Spay/neuter will stop this behavior, and it will eliminate the very real risk of reproductive tract cancers in females. Spay/neuter will also make litterbox training easier and more reliable. Be sure you have this done by a veterinarian who is very experienced with rabbits! If you do not know of an experienced "rabbit vet" near you, please check the House Rabbit Society Veterinary Referral Center.
Try to see the world through your bunny's eyes. Put yourself in her place. No one speaks her "language", she has been taken from her family and perhaps the only home she has ever known, and she has no idea whether you plan to love her, cage her forever, or eat her! You need to gradually and patiently earn her trust. It can take days, weeks or months, and depends on the personality of the individual rabbit.
Rather than being disappointed that the rabbit is not what you expected (it is quite possible that she will never learn to like to be held), take this opportunity to teach your children respect for an animal who is different from them, who has different needs, perceptions and behaviors than a dog or cat, and who is NOT a casual plaything. If the children really want something to carry around, they need a stuffed toy--not a live rabbit.
Finally, remember that the ultimate responsiblity for the rabbit's welfare belongs to the adults in the household--not the children. Most human children are pretty well into their late teens before they truly understand the necessity of constant, devoted care to another sentient life form. This can be your opportunity to get an early start in teaching them that all-important life lesson.
Your rabbit is a highly intelligent, potentially loving, loyal creature who can become a member of the family, if you allow her to be what she is-- a rabbit! If you and all your family can do that, you are in for the most delightful companionship imaginable.