I want to move a family of sims with parents, a toddler and a baby into..

The first thing you should know is that from what I can tell you can not move a married sim into another house. But if you want to get them divorced then try to move them in together again then here is what you do. (Note that I have never divorced Sims before so I'm not completely sure how it works, but there are other questions and answers on this site that could probably help you.)

First you need to make the house that you want to move them into vacant, so no one is living there. Once that is done click on it from The Town Map and scroll through the options as to what you can do with it. Soon you will see pictures of your Sims with 5000$ over each of them. That's how much it costs to move them. Click on it and your sim should be moved.