cats

Hi all, I'm kind of confused on this. My cat eats very slowly all day long. She'd go to her food bowl constantly throughout the day for a couple of bites and then back to whatever she does. I think we spoil her by making her food available at all times, my wife doesn't think so. She throws up here and there and I'm thinking because she eats too much. So, my question to you all is, how often do you feed your cat? Do you fill its bowl all day like me? Do you have specific times of the day where you give them a certain amount each time and nothing in between? I'm leaning towards doing the latter. Give her, let's say, half a cup in the morning and let her munch on it as much as she wants and the other half in the evening and nothing in between. She freaks out when her bowl is empty and starts crying and acting like she's about to die of starvation. Give her food, then she takes one bite and leaves. Bro, wtf. Lol. So any advice would be greatly appreciated.