Can you talk to her about this during the day and say that instead of having night time cuddle times you are going to have some day time cuddle time? So perhaps get some cushions, her favorite stuffed animals/dolls, a nice soft blankie, some books, and just sit for 15 minutes with her and cuddle, talk, read. I know this will be soooooo hard to do with a baby at home but I think it will pay off in the long run (can dh take the baby for a short time?). She is craving attention from you and needs to know that you are there for her still. She hears the baby scream and you go running to them. I think she wants to know you'll do the same for her. Obviously being up a million times in the night is not good, so instituting some really special one on one time with her might help.
Huge hugs to you....this must be sooooo exhausting.