Also, how would I go about introducing my cats to a new dog? I wasn't sure how to do it before, with Grim, and Diego got along fine with him, but Chloe loved to hiss and stalk Grim, but never touched him.
Sounds like you have one dog-friendly cat (Diego) and one nervous but mellow cat (Chloe). Thankfully no aggressive cats so this makes socialization with a new dog so much easier!
This is how I socialize dogs with cats, so far it's always worked well and we have never had either a clawing incident from the cats nor any dogs hurting cats:
a.) Get the dog used to the cat's smell. Do this by letting your cats sleep on a cloth or blanket first, then put the unwashed cloth/blanket in with the dog's crate bedding. At this point the dog has not yet met the cat.
b.) Switch the cloth back to the cats ... to let them get used to the dog's smell. I usually do this for the first couple days.
c.) Do the initial introduction safely. Put the dog in its crate and let the cat sniff around and see how they react. Do this until they seem calm around each other.
d.) Now you can move to a baby gate. Gate off the cats in their favorite room and allow interaction between the cats and the dog through the baby gate.
e.) Once everyone's comfortable with the above then you can move to interaction with the dog on a leash while indoors.
f. ) Once all on-leash interaction goes well you can try supervised off-leash interaction. But absolutely no unsupervised interaction ... not even "just for a minute" ... not until there have been many. many instances of consistent trouble-free interaction between the dog and cat.
g.) Afterward there can be very short periods of unsupervised interaction, but with you still in the room. This progresses to more loosely-supervised interaction as time goes on.
h.) Many dogs and cats will eventually get to the point where unsupervised interaction is the norm. Many times they will simply ignore each other, this is good! Other dogs and cats will be become friendly to varying degrees.
Cheyenne, my female Golden Retriever, "mothered " our cats and they adored her ... but I had socialized her with cats from the time she was a puppy. Our Wolfdog Spike absolutely ignored all our cats ... except one who especially liked him. He didn't "mother" that cat, but was happy when she approached and let the cat sleep in his bed with him. Spike was
not raised with cats from a puppy, only first introduced as an adult dog.
i.) Depending on the particular dog and cat, you may never get to the point of safe unsupervised interaction.
The last point was the case case with Marley, our Aussie/Rottie mix foster. He was never raised with cats, never had any cat companion in the past, and had never even seen a cat until he was already an adult dog. Despite repeated and very careful socialization, Marley just doesn't mix with cats because Marely has VERY strong prey drive. The cats like him, particularly our very dog-friendly Turkish Angora. But Marley does not see cats (even indoor cats) any differently than the gophers and ground squirrels that he has killed outdoors. To him they are
all strictly prey.
In cases of strong prey drive like Marley's, the dog must be kept separated from the cats at all times. Strong predation is not something that can be trained out of a dog because it's too strongly instinctual. Even if you think such a dog may be "trained enough" to resist it's strong predation ... you would still be risking the cat's life by allowing unsupervised interaction with such a dog. By contrast, Cheyenne the Golden had little prey drive at all, confining it to chasing tennis balls and frisbees. Spike the Wolfdog had some live-animal prey drive in that he would chase gophers and squirrels, but never killed any and he never chased cats as he did see them as different.
The idea is you want to socialize the dog to the cats and not the other way around. This is because although cats
are trainable, dogs are much easier to train! If the dog is bothering the cats too much then step back the socialization to the previous step. You can also use the "Leave it!" command to get the dog to leave the cats alone. If the dog is being fine but it's one of the cats bothering the dog, then YOU hiss at the cat. Sounds crazy but I swear it works when it's the cat who is the problem! When we hiss at our cats they
immediately stop whatever it is they're doing. It's not just our current cats, never had a cat that acted differently upon hearing it's human hiss at it!
Thoughout the on-leash and off-leash interaction, be sure to give the cats plenty of places to retreat to ... places to jump up off the floor from where they can "safely" observe the dog. It's always better to give the cat room to get outta there if taht's what it wants, you don't want a situation where the dog corners the cat and the cat has no escape. That's when you end up with a clawed dog.
If none of this works then I would try using Feliway (commercial product ... Google it), particularly if the problem was the cat acting aggressively. We so far have never had to resort to Feliway, but have heard good reports about it from others. If even Feliway didn't work then it would have go to management, in other words
never letting the dog and cat have
any unsupervised time together. Inconvenient yes, but not impossible.