Should I rehome my cat?

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I have a third cat even if no one wanted this. We rescued her because she had an injured leg. I have two male cats and she is female. The two male cats fight all the time. I have to separate them and they need to avoid each other. Blue is feeling better. He takes medication for seizures. He is very happy because he plays with my female cat. They are happy together. But this cat doesn't let me sleep. When I wanted to find a home for her no one wanted her. She wakes me up at 4 AM because she is hungry. I fed her at 4 AM. I feed her at 11 in the evening and five times each day. At 5 AM she woke me up again without any reason. I removed her from my room and she jumped on doors. She opened my mom's room. We need to lock all the doors, but my mom's door is old and can't be locked inside. So this cat is entering her room too. If I want to keep her in another room she jumps on all doors until she can open the door. If I lock the door with a key she is trying to break the glass door. So I don't know what to do. She meows in the morning and doesn't let people sleep. My mom and I are upset because we both had sleep problems. And this happened every day lately. Should I rehome her? I will add a picture of my three cats. My cats seem too spoiled and they don't understand the word 'no'. And now they don't let us sleep. But Sissy (this is her name) is like a feral cat. She can't stand to be touched by strangers. She doesn't accept my mom and she is too attached to me. She is very anxious. She paces up and down all the time and she seems anxious. This happens when she is hungry. Maybe I should take her outside on a leash. I don't know what to do. The vet doesn't know what to do. Her behavior started after she was spayed. She became an anxious cat.