slitty kittay, those pics remind me so much of my own guys! I've got 2 cats, one dog, and Jake (the dog) only pays attention to Buffy. If he sees Willow, he'll give her a look and then either ignore her or ignore her and pay attention to Buffy. He's learned that he can get a reaction out of Buffy. If Jake so much as walks into the same room as the cats, Willow will just freeze and stare, while Buffy will immediatley puff right up, arch her back, hiss, and "mreowl" at Jake in such a menacing way. So who's Jake gonna pay attention to? You got it.
As to the topic at hand, Jake is an Australian Shepherd X Border Collie cross, so he's got some strong herding instincts. It wasn't until late last year (or early this year, I suddenly forget, lol) that he learned to ignore both the cats. 6 1/2 years of sweating whenever Jake was in the vicinity of the cats while off-leash. He now ignores the cats, because, as we figured out, he's only ever paid attention to the cats because we did. Jake's very willing to please, so if he sees us mad at the cats or trying to scold them, he'll jump right in and be mommy's little helper. If the cats do something bad, we'll just ignore them and continue what we're doing. Jake sees that, so he copies us and ignores them too (though he might keep one eye peeled on them, but his head will be on the floor like he's napping). So now I can trust him enough to let him have free range of the house while off-leash, while the cats are roaming free as well. Heck, I did it once during the night, asleep (my door open because his crate is in my room). I didn't wake up to blood all over the walls, lol, just a guilty dog that decided the couch was a comfy place to sleep
. However, we still have issues about getting Jake to ignore the cats while outside. I'm not sure I want to even work on it, because both cats are such escape artists and Jake really helps me a lot when they refuse to get caught (Willow freezes, so I can catch her pretty easily, but Buffy loves to cross onto other neighbour's lawns, so Jake acts as a "wall" when she wants to get by). Of course, I always make him go into lie-down so that I will always have some control over him (and it makes him hesitate when he sees the cats when I'm not around, because part of him is used to lying down when they're around, and he can't quite decide between obeying my training or giving in to guilty pleasure and chasing the cats).
If your Border Collie is the willing-to-please type that reads you quite easily, then you might be able to just ignore the cats and he will too. Of course you gotta train him a bit first. I drilled "No kitty chasing!" into Jake's brain, simply by yelling at him when he chased them or leading him away whenever the cats were around. For extra protection, I've taught Jake that when Buffy makes ANY kind of sound at all (growl, meow, mrowl, hiss), Jake has to back up or go away. If he doesn't back up, he feels like he should be doing something anyways (due to repeatedly enforcing the command), so he'll sit instead. Good enough for me, though if Buffy makes another sound of displeasure, I'll make Jake back up or go away. I want him to have no more than 2 warnings. 1st warning, he HAS to obey Buffy. If she's still not happy, he's gotta do better (if he sat after the 1st warning, he HAS HAS HAS to back up or go away, no ifs, ands, or buts. Buffy's the boss over him [or so I'm trying to teach him, lol])