So glad to hear you're committed to keeping this dog even though he isn't perfect!
Too many people want instant gratification and dump dogs if they aren't like Lassie the minute they bring them home.
As for the cats....can you put a chain on a door of one room, so that it opens only wide enough to let them get in the room? You can put all their stuff in there. This way, they know they have a "safe place" and that will boost their confidence and help them get used to the dog.
Teach the dog to "leave it" and never let him chase the cats.
This is all a big adjustment for everyone, but with patience, consistancy and training - it should work out!