Keeping the family tree?

If you move ALL of the sims in the family tree together to the new world then the family tree will remain.

If you have mods there are easier ways of doing this.

I imagine most of the families in your world would be related in some way by the 5th generation so I think the best way to move everyone to a fresh town would be to use Nraas Porter. There's a tutorial at the Nraas site on how to use Porter. It's quite easy to use but there will be some reshuffling of sims when they are unpacked in the new world. I have found most families are kept intact but the odd sim gets separated.

Another approach is to use NRaas Traveler to move some of the sims to a new world, thus keeping both worlds in play within the same game and having the ability to travel and move sims between them. Family and other relationships across the worlds will be preserved this way. Even if they never intend to play the current world again and would be using it as a source of visitors (for a while) and sims to pull into the new world using MasterController, many players find this way to be satisfactory as well. The currently under-performing world should not drag down play in the new one because only one world can be simulated at a time.

For long-running multi-generational play, many of us find that NRaas Overwatch and ErrorTrap (plus Register, Traffic, and to an extent GoHere) are indispensable to keep things running smoothly.

Without the mods, much of this is not possible because in that case moving to a new world means essentially starting over (in many ways).

How much of the family tree do you want to keep? Everybody? All the Aunts/Uncles, Cousins, Nieces, Nephews, etc? Then as mentioned, you have to move everybody. Or use a mod.

If you just want to keep the ancestors, Parents, Grandparents, great-etc, then you just move them. If they are dead, you need to collect up the gravestones from the graveyard or where ever and move them too.