Re: Not try to play w/ or heard cat?
I think alot of it has do to with your cats and how much they will tolerate as well as your dogs. I worked on this with Dex for a very long time before it started to get better.
redirecting is a great idea, interrupting the bad behavior (chasing cats) and redirecting to an appropriate behavior (playing with toy). When i did this with dex he would hold the toy in his mouth and still chase and bug my cats, at least this way he didn't mouth them.
You can always try and prevent it too. When your dog locks on the cat and starts the eye/stalk thing you know where this is leading, thats your chance. You can stop it before he gets the chance to chase them, maybe give him a handful of treats for sitting and looking at the cats but not chasing, or even better redirect his prey onto a toy and play an fun game of tug or fetch, and lots of praise . Have you ever used a clicker with your dog? Those can be very helpful as well when your trying to prevent the chase, just a nice consistent sound that always means to your dog hes doing right. We had some success by doing this.
We actually ended up adopting a cat that was extremely socialized with dogs and a bit of leader. (the crappy people who brought him to the rescue threw Ellie and his kitten mates in a large crate with a bunch of dogs to bring them to the rescue,) That ended up helping us a ton, this cat was not bothered the least bit by Dexter's attempts to chase mouth and herd. We then knew our dog was not really out to KILL the cats and those two ended up becoming great Pals
As for my female cats who had to tolerate his puppy madness aren't so forgiving, We had alot of improvements but Leave it was still very very selective with testy teenage Dex, and my two female cats.
One day, I was getting both dogs out of the car at my parents house Dex saw a bunny jumped out before i could stop him and started to chasing a bunny into the road, Leave it meant nothing his fav toy that i always carry around (used to redirect him from most anything other dogs/bodies of water ect...) meant nothing, that was really scary, this prey drive has become life threating, I could of lost my dog and i knew it was time to get some professional help, we also had a barrier frustration issue brewing we needed some help with.
We went to a master trainer. With guidance and supervision she trained to how to use a prong and a vibration/remote collar. I am very much into the softest method possible and love positive training, these tools sacred me, when dex was a puppy i swore i would never ever put anything like that on him ever, i believed EVERY dog could be trained 100% positive and it would work.
Ive learned so much while raising Dexter. With my dog it required me to find a little more of a balance with my training Dex needed a consequences to some of his bad behavior, espeicaly when it becomes life or death. Although we stay very positive and still love to use motivators and everything, we just need to sometimes have stronger consequences. I can't refuse to try a tool that could save his life. I just needed help learning how to use the tools so i could be as fair and gentle as possible with him.
We have had HUGE improvements since then, a Verbal Leave it means something the first time now, and now that mom has some sort of backup for dangerous bad behavior its overall improved our relationship. I would suggest trying the softest methods first really taking some time with them, some dogs do great with it, if it becomes dangerous to your dog or cats safety then maybe consider going to a experienced trainer. Best of luck, I understand how frustrating it can get, but with consistency time and fair training anything can get better