YABVU!
She is your cousin, not your sister. No matter how close you two are, you will never understand the relationship she has with her mum. You will never know everything that's happened nor everything that's been said. Hence, you may not understand why she doesn't like you speaking to her mum, but you don't have to understand. She's in a bad place, and maybe she can't explain to you right now, or maybe it's just that she's being loopy, but even that's understandable.
I do agree with the other posters, too. You don't seem to get the fact that it's not about you. Everything you have posted has come back to you - how you were deleted from her FB, how she's ungrateful because she wont talk to you, how she's not speaking to you, that you don't know what to do etc. How about taking a step back and looking at the bigger picture - she needs your support. Everyone says and does things the don't mean. It's bad enough that she's in an abusive relationship, which will screw with her mind as it is, but if she's heavily pregnant too her hormones will be all over the place, adding to the mayhem.
My advice would be to sit down and write 2 letters. In one letter, write everything you feel angry about the situation, what annoys you, how you feel etc. Once you've done that, write a second one to your cousin, also explaining how you feel but in a calmer way, focusing more on how you want to sort the not-speaking-to-each-other situation and how you want to help her than how you think she's being a git (from what it sounds like you do want to be there for her and that's great!)
Burn the first one, give her the second one. I'm sure that she will appreciate it even if she can't express that gratitude to you right now.