"Punishment" is not in your cat's vocabulary. Positive reinforcement of good behavior -- with treats, attention and verbal praise -- solves most kitty behavioral problems.read more
Good for you for adding another cat to your family. It’s important to note, however, that unlike dogs, cats are not true pack animals and cooperative hunters. Wild cats hunt by themselves and spend a fair amount of time protecting their personal turf.
Your adult cat had her lap, her toys, her food, her litter box and so on, and sharing these things with your knew kitten is most likely not easy for her. Multiple cats will typically negotiate territories with each other, even if they get along. Your older cat likely doesn’t think she’s been replaced but rather that she has to be a bit more wary. You probably also spent a lot of time with your new kitten, so your adult cat may now be conditioned to expect less attention from you.
Try to engage both your cats in activities that you can all enjoy together, such as playing with a fishing-pole toy. Make sure all is well at dinner and litter box time. Your older cat may also be reacting to your kitten’s scent, which serves as a territorial marker, so you could try washing your hands and laying down a fresh lap blanket when spending time with your older cat.