To answer the question, if you want to communicate with kids 700 miles away (outside of commercial communications grid), you will need an amateur radio license (FCC), a high frequency (HF) transceiver, long antenna (long piece of wire) and a firm understanding of how radio waves propagate through the air, over the horizon and reflect off the layers in the atmosphere. The people you want to communicate with will have to do the same thing.
Here is how to start.
Find a amateur radio club and go to some meetings. It is worth a 90 minute drive to be involved with an active club with members that are dedicated and enthusiastic about the hobby. Your kids will need to do this where they live as well. Kid's willingness to attend an amateur radio club meeting is a good measure of how well your communication efforts with them will work. The cost for this is $0
You and the kids will need to pass two licensing tests so that you can legally have access to the frequencies you will need to talk 700 miles. The first exams is for a Technician license ($15-$25). The frequencies a Technician license can access lets you consistently talk about 50-75 miles with a good antenna. These transceivers are cheap ($25-$500) After you pass the Technician license, the next exam is for the General license($15-$25). The General license opens up loads of frequencies that let you talk around the planet with the right conditions. There is a third license level call the Amateur Extra which opens more frequencies but is not necessary for what you want to do. The wavelength of the frequencies the General license opens up can be longer than a football field. It is the nature of these frequencies that lets them bend around the horizon and bounce of layers in the atmosphere.
Next comes the hard part...picking a HF transceiver...lots more expensive ($1200 and up)....I've had a general license for a couple years and still have not picked the one radio out...I picked up a used HF rig at a garage sell and it will do what you want to do. That was a fluke though because active amateur radio operators can smell garage sale radio equipment even when up wind.
Once you and the kids have licenses, transceivers, antennas and a little knowledge, them comes the practice, then practice, then practice. You and the kids will need a plan to communicate during grid down and be capable of operating your radio rigs without the internet, youtube, online manuals, forums...or anything like a telephone. Oh and y'all will need to practice some more.
Now is the best time to get your knowledge and gear. I'm in a couple of amateur radio clubs and they do things like send email across the country without an internet service provider, receive NOAA weather satellite images, send and receive faxes over the air without the help of Ma Bell, send pictures, forms and documents over the air. We do field days and mock disaster drills with the area hospitals and emergency response activities. Anyone can do all of the for less than $2000 brand new equipment, some patience and a couple of licenses. Anyway the time to learn is now before the grid goes down.