Neighbors cat keeps having kittens at our house..

I’m in a dilemma, my neighbors cat hopes the fence and hangs out with my male (fixed) cat. Eats our cats food and Is here probably more then at my neighbors house I don’t mind that the cat is here I’ve even named her and pet her (when she lets me she kinda sketchy with letting people pet her). When I first noticed her she looked like a skeleton she was so skinny and now she looks like a healthy weight. The problem is she is now just had her third litter of kittens on my property that I will now have to take care of and try and find homes for. I want to bring her to get fixed because but she is not my cat and I don’t know if I can even catch her and bring her to a vet without her freaking out. What should I do?