I have this similar problem with Stephano, who HATES all dogs, except my dog, but that took quite a lot of work to get him ok with her. After much work, she does accept my dog, but if my mother in law brings her dog over....and she is small and is an angel to all cats, Stephano freaks so bad.
You have to realize, if they were feral and outside, their experiences with dogs was not good. They have been chased by dogs and fought for their very lives to get away from them. This is not something to easily change after you have a cat that has had these kind of experiences with dogs. It may be possible to get the cats to tolerate your mom's dog, but it may not.
What worked for me to get Steph to tolerate my dog....and she is a big dog, a doberman, we put up a baby gate to block Greta away from the cat, that way the cat knew that Greta could not get into his room to her. I was lucky, STephano let me hold him without clawing me to death and I was able to hold him and talk soothingly to him and Greta, I'd say "this is a nice doggie, see, she won't hurt you" in a very quiet, calm tone, and I'd get a little closer to the gate with him in my arms. Eventually they touched noses and Stephano would bat at Greta, no claws, and hiss alittle and I'd say "no, no" (in a very calm, hushed tone...not yelling at all) "this is a nice doggy, she won't hurt you, see, she is very nice". We had sessions of these little lessons for a few days, and cat and dog got treats during these sessions. Treats let them both know learn that this is a good experience. WIth the treats and the voice, and some time, we eventually got to the point where we had the dog on a leash, in a down stay, and let Steph walk around her, they both got more treats, more praise, LOTS of calmed talking during the whole thing, and they are best buds now. For the first few months, ocassionally Stephano would hiss and smack Greta, with no claws, if she nudged him by surprise, but he doesn't do that any more. And we never left the dog alone with the cat, ever, ever, ever, like when we left, cat went to his safe room. We still put him up in his room if we will be gone for a long time, just to be safe.
It is possible sometimes to teach them to get along. I can imagine it would be harder though if the cat was able to go outside, because I can imagine them being scared away. I think I said your mother's dog before, but I think it's actually your daughter's dog? If it were me, personally, I would just tell her not to bring her dog. I know this sounds harsh, and it's her baby, but your cats deserve to feel safe in their own home. I actually told my MIL to stop bringing her dog with her, because Stephano goes insane with she brings her dog. He actually will stalk the dog and try to attack her, even when she is sitting quietly beside her on a leash. She used to bring her over all the time and Stephano only has a 5 hour window of time in the evening when he is out, before he goes to his room for the evening (because I have another cat that can't be out with him) and I didn't feel it was fair for me to shove STephano in a room during his free time, so she could sit here with her dog for her 2-3 hour visits, so I told her to please not bring her dog. I know the dog is her baby, but I would not feel bad about doing it. Either that or be prepared to lock your cat up in a room every time she comes over with her dog, and expect that the cat is going to be freaked for some time after she leaves with the dog. In my MIL's case, she is home with her dog 24/7, and she lives 2 miles away. I feel like she can leave her dog home for a few hours, it will not kill her or the dog, but it puts too much stress on my cat, in his own home, even though her dog is fine with cats and is not the problem. Cats will be cats. They are not reasonable creatures