First off, welcome to the CoE Community...
Death is handled a little different in CoE that in other games. Many think this may be a perma death game and it's really not. Death takes 3 forms, from bring knocked unconscious, to coupe de grace, then perma death. You have a fixed amount of spirit and if someone does a coupe de grace then you will loose spirit depending upon the number of deaths and your fame. When your spirit is nill then that would be a perma death requiring a new spark of life to continue.
If you married another player then the wife's character will have the 3 forms of death just like you and would likely not suffer a instant perma death. As for as your children, they can not be killed till they come of age, then they are very vulnerable.
Now if your wife is a NPC and someone goes on a killing spree then you will loose your family (kids can not be killed at present). So if that was to happen you will survive through being knocked unconscious or a coupe de grace however your adult family would be dead. As in real life you may have to find a new wife and have new heirs if all the family is adult. However your Character will still be alive and you can rewrite your Will to address your new family and situation.
Now as for an adult family they may not all be under the same roof. When your children came of age they found a wife of their own and moved out to start their own life. These characters can be utilized if you find yourself in a perma death for some reason, just take over your child and have a new wife.
While finding a spouse would be a pain in the butt to do, starting a new family I don't feel would be that hard of a problem, it just may make you a older parent which would result in a younger character when you take them over.