Sims 3 keeps freezing randomly for a few seconds (help)

You need to elaborate a little more about this.

1. How big is this new family?
2. Is it a generic game family or is it one self created/one others have created with? Beware of presaved characters saved from other game plays as they may have all sorts of stuff in their inventories. We learned this the hard way with Kirry Bixley Simnel having the entire fruit and veg harvestable contents from one of Rflong7/13's world ...
3. How big is the world you've dumped them in. Come to that, what world have you dumped them in?
4. Is this utilising an old game save in any way? If so, it may have 'bloat' needing cleansed.

In short, there could be any number of reasons that's bringing your poor PC to its knees trying to process what you've opened up, you need to say what you have tried so that by a process of elimination you can find out the cause.

By the way, you may get a faster response putting this query in the Sims 3 Technical Issues section.