Because you’ve created them as separate collections, they can only be bound to separate collection lists. That means, you’d have to do custom script to merge, sort by date, and then truncate the combined list to 3.
A better way is to have one collection called “Blog”. In that collection you’d have an Option field, or a Ref field that separates Cats & Dogs.
That way you can have a cats page just showing cats posts, a dogs page just showing dogs posts and you can easily show the 3 most recent on the homepage.