Rabbits often don’t enjoy being picked up and handled unless they’ve got used to it from a very young age. Rabbits who aren’t used to being handled can bite, scratch or even kick their owners. However, rabbits who’ve been handled from a young age can make very good pets.
Rabbits will often enjoy being petted on floor level rather than picked up to be cuddled. If you or your children would like a small pet who really enjoys being picked up and cuddled, consider getting rats or ferrets who love spending time with people.