M.P.
Let go of the need to be right or to say the other person is wrong. Say it's just not working for me right now and stop trying to communicate. You don't need to tell your Dad that you're unfriending him. As you learned doing so created more drama.
Deal with your feelings with yourself. Talk with friends, not other relatives. And get into counseling. You have a whole lot emotional turmoil going on in regards to your family. Let them go and work only on yourself, finding ways to feel better without needing to be connected to them.
When you tell them you're cutting them off you're still maintaining contact. It's negative to be sure and we know that negative attention seems better than no attention at all. Focus on your immediate family. How wonderful that your daughter crawled. Don't let your Dad and sister take away your happiness over your daughter. You're giving them too much power. Take care of yourself.
Reading up on co-dependency may help you put all this in perspective. My first therapist gave me a book to read on it by Gay Hendricks and it helped me tremendously. It did take many months and even years to work it all out but I'm so much happier now.
Of course you're needy. You need to feel loved by your Dad and sister. You are having to accept that they're not able to love you in the way you need them to. It's time to mourn. You've lost the fantasy that they'll do right by you. They just aren't able to do what you need so you have to find other ways to feel loved.
Later: I suggest that you talk with your doctor about getting started on an anti-depressant to help you get past the immediate pain. This will help you get started in crafting a way to get past this first stage of emotions.