What are the odds your family isn't all on a single cellular carrier, making you unable to take advantage of such redundancy?
Verizon and Sprint are compatible, while AT&T and T-Mobile are compatible. And with them all switching to LTE, it's likely they will all be mutually compatible in a few more years, when manufacturers start selling multi-band LTE phones.
Most every post-paid cellular plan includes voice roaming. Even if you're not paying for roaming normally, when you dial 911, all restrictions are dropped, and your cell will connect to any available tower from any provider that it can.