Goats have a little more brains than sheep and treated right, can be easy and make great pets. The bad thing about goats is if they do get out, they will eat and ringbark every tree that you have. Sheep are more grazers, meaning they wander and always want to get through the fence even when there is plenty to eat. They also have more problems with flystrike, footrot etc. If you get a young goat of a nice breed, you should be able to teather it and your wife will find it much easier than sheep overall. My friend has a naughty ram that I'm trying to convince to put into the freezer in the shape of chops. He keeps nocking her over with her shopping.
You can lead a dog to water, but you can't make him a horse.