It's hard when that happens, especially when your relationship changes with an existing pet.

I have that with Mini and Jasmine. Mini is very demanding of my time. He greets me first when I get home, follows me until I pay him enough attention, follows me around the house and butts in when I'm playing with Jasmine. Then Jasmine gets upset because she feels left out. But if I greet Jasmine first and pay her attention, then Mini gets seriously offended and quite sad. That breaks my heart as well because he's a mummy's boy. I can't always play with them both at the same because they fight like crazy sometimes.

What I do is wait until they are apart, then visit Jasmine and spend time with her. It might just be sitting on my lap while I'm on the computer or having an afternoon nap while Mini isn't around, but she seems to appreciate it. And we have our little secret times, like when she sits on the bathroom sink while I'm brushing my teeth.

It seems to balance things out. Try not to feel too guilty, a new cat changes all the dynamics in the house and will take some time to settle. Good luck.

PS yes, they can be spiteful! That's the difference between cats and dogs