Hello,
Im wanting to move some families with their houses over to my Lucky Palms world/neighbourhood from other worlds/neighbourhoods for example like Roaring Heights and Barnacle Bay.

How to do so in game without causing too many problems? Thankyou

I don't know how other people do it, but when I did it, I saved copies of the houses to the bin, and placed them in the new world as empty lots. Then I used Nraas Porter ( https://www.nraas.net/community/Porter) to move the families. Porter does a very good job in my experience of preserving relationships within and between households. I know the gamne has an option itself to save inhabited lots but it doesn't fill me with confidence.

You could simply save their families along with their houses to the library, then place them down to your preferred world. Use Master Controller with cheat module and ErrorTrap to repair their relationships and family trees.