I'm sorry you're upset
I'm not totally sure but I think any snipping at other animals while they are eating is food gaurding or food possesiveness.
I think it does need correcting, maybe you could hold the cat while Layla is eating and give Layla treats while she's nice and calm?
There are a lot of techniques that can help with it. It's such a natural defence mechanism that it's really common in my experience of talking with trainers <3