Cat Advice!!! Helpppp 🐈

So I have a sweet girl kitty who got pregnant in the middle of a big move our family made. Well she's had her kittens, 4 of them all perfectly healthy and precious, and it's been about a month since she gave birth. The only problem is that for this entire month she's been driving my fiance and I CRAZY by meowing urgently nonstop every time we stand up to walk around. And it's very loud, insistent meowing that sounds like she's upset but really all she wants is for you to give her milk or fill her bowl. But she'll do it even if her bowl is full of food. She obviously can't eat as much as she wants, though I have added an extra feeding time for her every day since she's feeding baby kittens. I'm just sad because she's gotten so bad that my fiance is saying he's going to get rid of her in a week if she doesn't stop. And this is my baby...I can't stand the thought of giving up on her no matter how annoying she's being. So I'm hoping someone on here knows maybe what she needs that would help? Or what to do to get her to stop? We don't feed her whenever she asks, so I dont think that's the problem. She only gets food at mealtimes. It just really is getting exhausting and I don't want to lose her