No you do not have to stay at your home resort. However, you do get a booking advantage at your home resort. You can book your home resort at 11 months prior to the trip and you can book the other resorts at 7 months. So, if you want to try a different resort, then I recommend booking your home resort at 11 months and then switch it to another resort at 7 months. That way you will have a reservation if the other resort isn't available.
Also, please be aware that there are times of the year where booking at 7 months can be extremely difficult and it may be impossible for some of the resorts. For example, the begining of December is extremely hard to book at 7 months because it is so popular.