Oh wow..that makes me so sad to think about them giving advice like that to people who don't know any better and who think they can trust their vet to guide them.
As far as the nails - each of my kitties needs something different. Sam has always been good about it, but he insists on standing up, and I have to do one nail at a time and let him put his paw back down in between. And he gets a treat after every couple of nails. We are always sitting on the carpet and he usually leans against me while I trim them. I rarely do his back paws. Atticus was a very long process to get him to let me trim his nails. I have to brush him for awhile first until he's super relaxed. And then I have to tell him what I'm going to do first, show him the clipper, talk to him in a quiet low voice, and if he starts to get anxious, stop and brush him some more. He couldn't care less about treats so it's all about the brushing with him. He doesn't take care of his back nails, so I do have to trim those too sometimes. But since he is laying down when I do his nails, it's easy enough to work my way around all four paws.
So it's just a process of figuring out what Gracie needs in order to let you do it, and as you can see, it's not quick with either of them. But I figure if I factored in the time it would take to get them in the car, drive to the vet, and come back home, it's still faster to just do it at home than all of that!