Could it be that you're so angry because you're taking what other people do or don't do as something personal to you? You seem to expect people to do what you would do when in reality we all handle life differently. It might help to work on feeling compassion for them and their circumstances. Instead of telling yourself that they have rejected you or are causing your life to be complicated you tell yourself that they, just as you, are doing the best that they an do at the moment while you remind yourself that they have different lives than you do.
For example, the friend with the new baby may have had a difficult delivery, may have depression. Actually, may have been dealing with depression since the birth of her second child and not really be aware of it enough to tell you. Depression, even not so serious depression often causes people to withdraw. Also causes them to not be able to cope with several things at the same time. I suggest that her not wanting to talk with you probably doesn't have anything to do with you.
I, too, would be lonely and disappointed in your place. I've had similar things happen to me. I've lost touch with several friends since I retired even tho I actively tried to keep the friendship going. A change in life circumstances can change friendships. I found that it was time to make new friends and know that doing so is not easy.
As far as your sils go, their lives are definitely much different than yours. I suggest that the one who is having her parents raise her children has a serious problem. Sounds like she's not capable of caring for them herself and her parents have continued caring for them for the well being of the children.
I don't understand why they don't make room for your children. Have you talked with them in a calm, non-judgmental way about how you feel about your children not being more involved with them? Don't talk about the reasons for them having their daughter's children. Just talk about your and your children's relationship with them. Is your husband concerned and has he talked with them about his children? Again, it's important to not say anything about the sister and her way of taking care of the children. I suggest that she is taking care of them the best she can by having her parents care for them.
Your comment to the other sister about why she'd want to spend time with her ex does, frankly, sound insensitive. A lot would depend on your tone of voice. You perhaps could ask that question by prefacing.it with a comment about your concern for her and how she's feeling. And ask it in private with time for a sympathetic conversation.
Because of her temper tantrums and mood swings I suggest that it's very possible that she has a mood disorder. I've had much experience with bi-polar disorder and depression and know that the person who has these disorders is miserable much of the time and very sensitive to remarks that are not intended to be critical. Being in relationship with them is rightfully compared to "walking on eggs." Also, funerals, are highly emotional by themselves. I have found it best to have light conversation unless someone wants to get more serious.
I suspect that you are young, in your 20's and are inexperienced in how to manage in these sorts of situations. So don't beat up on yourself. Your asking the question suggests that you are wanting to learn a different way and I praise you for that. Where there is a will there is a way. And......we all make mistakes as we learn. I'm still making them at 67. lol
I suggest that when you are able to be gentle on yourself you'll find it easier to be sympathetic with others. When I was in my 30's I realized that I was angry most of the time and started therapy after my first failed intimate relationship. After several years of therapy/counseling and reading of self-help books I was able to gradually let go of my anger. I found that I first had to feel compassion and then I wouldn't be so angry. The actual lesson that helped me the most at first was learning to not take what people did or said personally.
This involves learning about and forming boundaries for ones self and then being aware of and respecting other people's boundaries. For example your friend said to not call but yet you did. And when she repeated her request you felt that she was rejecting you and why would she do that? Must be something you did. Right?
I suggest that the reason for requesting no calls and the message on her voice mail had nothing to do with you. Her calling and personally telling you to not call was the result of your crossing her boundary. Boundaries are complicated and difficult to understand. I needed much help in learning how to have them and how to respect them, both mine and those belonging to others.
In counseling, I learned that anger is the result of not being aware of more tender feelings. It took me time to find my more tender feelings. In the end I learned that for me the anger was covering my chronic depression. The more tender feelings I wasn't aware of were compassion for myself and others. I was living in a world of shoulds and should nots. Law enforcement was a natural career choice. Law is primarily black and white. However, I had to deal with people in all sorts of conditions. The career its self is far from black and white. This "forced" me to make personal changes so that I would be comfortable.
Perhaps having these experiences is pointing you in the direction of counseling. I suggest that you will have better relationships once you figure yourself out. I urge you to find a counselor with whom you're comfortable working with.
In the meantime focus your attention on loving yourself. Take care of yourself. Do nice things for yourself without expecting anyone else to participate. Praise yourself when something goes well. I started doing that out loud when no one could hear me. "Good job, M.! Dinner was delicious tonight." otherwise they might take it as a sarcastic remark. If I wanted praise from some one else, I'd say something like, "wasn't dinner good tonight?" or "I'm pleased with the salad! I tried a new recipe."
When I felt bad because I'd said something that made someone else angry and they wouldn't accept my apology, I'd remind myself that I didn't mean to hurt their feelings or make them angry and.....that how they took what I said is their responsibility. "I am OK! I learned something from that experience."
I believe we are alive to learn and grown. It's a life long adventure. I don't remember who wrote this in a poem but I am comforted by it. "I have miles to go before I sleep." Be kind to yourself. Live is a long road. We can travel with a sense of learning and adventure. You will have many friends over time. Some will be friends forever and some will drop by the wayside as their lives change. Also, as your life changes. Since you haven't spent much time with Dawn, you don't know if you still have things and/or ideas and feelings in common.