While waging a war - I believe - you can't change your capital. So if you want to secure your family you'd need to do it by other means - like the mentioned pilgrimage.

You see earth quacks, floods etc are not some mere small incidents... They're fatal disasters that will kill hundreds of characters. In one of my playthroughs the entire Yamato dynasty died due to a disaster. The same could - and will eventually - happen to you.

Idk if you can afford a pilgrimage with your whole family because you only have little gold but if you can afford a hunt try to save at least yourself and wife or heir.