Are GPS-tracking apps data dependent? Are GPS-tracking apps data dependent or will devices use GPS signals alone, to notify their locations?

I am looking for a GPS-tracking app to track family members on a trip where we gonna have limited network coverage, and in some areas no coverage at all. 

I am not sure if these apps need data connection to send the location to another device, or they would only use GPS signals.
While a data connection might prove helpful for a faster fix (see: AGPS), it's not strictly necessary to have one. There a a lot of "Offline GPS Apps" available. I personally e.g. used Locus Maps successfully for that in the past, but there are plenty of similar apps available.

Tracks can be stored on the device, of course, and do not need to be sent to a server for the tracking process itself. Most apps allow to export them later in GPX or KML formats.

If, however, you want to now the position from a "remote device" (as your updated question shows, to e.g. know where your kids are at the moment), that cannot work via GPS alone, as GPS signals are only received by our devices, not sent. So this requires at least some kind of coverage: solutions are available to exchange data by different means, e.g. via internet (requires mobile data) or by SMS (still requires a network signal).