We've had some 'cat/dog' issues in this house in the past
We have two rescue cats and when Daisy came home as a 6 month old rescue it all went VERY wrong. To cut a very long story short one cat lived in our bedroom for about 6 months and the other became known as 'the roof cat' as she went in the garage roof and refused to come down except at 2am when she knew Daisy was locked in the lounge, even then she would go again by 5 am!!
She did that for a year and then suddenly one day walked into the house at 6pm stood in front of daisy and 'shouted at her, lay down infront of Daisy as if daring her to do anything. Daisy stood like a statue until the cat moved
We have not looked back since and the roof cat now slinkies round Daisy and is her best mate
Then 4 weeks ago we introduced Dill another 6 month old rescue - people who knew the cat saga thought I was MENTAL to risk it again!!
It took less than a week for the cats to be ok. I did panic at first because both cats took up their usual positions of under the bed and in the garage roof but as I say within a week they were back. They are still not as relaxed with Dill as they are with Daisy but they dont know him yet
I truly believe that the second time around was easier as the cats were used to Daisy. I dont think you have anything to worry about as your cats are ok with visiting dogs and if you make sure the cats have 'sanctuary' places that the dog cant get to you should be fine. I still have cat beds on the top of the kitchen cupboards, we still have a high table in our bedroom (very attractive - NOT) and I cant praise the use of baby gates enough.
They allow the cat to move freely about the house whilst stopping the dog in its tracks, that way even if a chase does start the gate stops it. The cats soon realise that the dog cant get under (as long as you mke the gap the right size
) We have two gates one between the kitchen and the utility where the cat food and litter tray are, and another between the kitchen and the hall so the cats can get upstairs without being followed.
HTH