There are a few ways to make this happen, this is probably the easiest:
Manage households>filter using the 'show' filter>locate pets household and click the double arrows -'Transfer Sims between households' button>click on the pets to move>filter to the world where the household to move them into is or if it is a NPC household that is not housed use the 'Not In World' option>click on one of the members who lives in the house you want to transfer the pets into> then make sure the arrows are pointing the correct way with pets and sim highlighted and move the pets into the 'new' household> click the large tick at bottom>done.
This seems confusing to read but if you have the game open and just follow along it should be easy for you.
If you are having trouble finding the household you want to move the pets into make use of the filters and filter by 'individual world or Not In World' and also 'played or unplayed' and 'My favorites or other' then scroll until you see it.
Carl's made a guide here on how to move sims which is just the same process:
http://www.carls-sims-4-guide.com/tutorials/moving-sims.phpThe guide is a little simpler than my instructions as back then (when the guide was made) filters weren't as detailed but it does explain the basics anyway.
Just remember you need to have a pet/sim chosen from both households so you can then choose which way to move the selected pets/sims.