When my mom is at home she refuses to go anywhere, but when she travels she'll do anything. How can I get her to be more active?

Limited World Question: It so seems that my mother, who is 79 and has lived with us for 18 years, continues to make her world more and more limited. We continue to attempt to ask her to go to lunch or simple things with us but she always refuses. Contrast that with when she goes to visit my brothers in another state, she'll go to baseball games, professional sports games, to others homes but when she's at home she flat refuses to go anywhere. It's very frustrating seeing her on the couch, clearly bored out of her mind, when in another setting she'd be going with them. I believe she is clearly punishing us somehow? I'd like to think of this differently so ideas are welcome.