Holly, I would advise talking to your vet. You need to clean the areas your cat sprays with a good enzyme cleaner, not just to wash it, as ordinary washing doesn’t remove the smell for your kitty and she can tell s/he’s sprayed there before. If you have trouble seeing where he (is it a he?) has sprayed, then a black light will help. If it is a he, has he been neutered yet? Cats can be very territorial and neutering helps dampen down both the territorial and spraying impulses. (Was your cat neutered later in his life? If so, then he may already have learned to spray before his neutering and the habit may be more ingrained.)
I would suggest Feliway, as it has worked well for my own cats. A Feliway spray sprayed every day (yes, I’m afraid it does get a bit expensive) on the spots where your cat sprays tells your cat that ‘everything’s fine, we don’t spray there’. It’s not a drug, Feliway is a pheromone that imitates the pheromone cats release when they feel safe and happy and secure. Second, each time your daughter comes over, I would plug a Feliway diffuser into the room your cat likes to be in, or, alternatively, in the room your daughter is in if your cat spends time in there too. Again, it just reassures your cat that everything is fine and there’s no need to freak out. It really does work for my cats when they’re stressed out, they both gravitate to the room where the Feliway diffuser is, they love to be near it.
I am a little concerned about your cat’s reaction as normally cats are interested to smell other kitties on other people and don’t regard the smell alone as a threat. Is your cat particularly nervous or has it had bad experiences with other cats or particularly your daughter’s cats? If the Feliway doesn’t help, then I do think you need to talk to your vet, as your cat seems particularly distressed and a short course of kitty prozac might help to alleviate his distress. It seems a bit drastic but so does your kitty’s reaction. Best of luck.