We went through this with our older one when we tried to get him read something he didn't care about. Our fault, we didn't realize at that time. DS4 went through a long stage where he would read with my husband but would stop as soon as he saw me. Fortunately he no longer does it.
We too take turns in reading, either one page each, sometimes he just reads the first paragraph and we read the rest of the page. He reads simple chapter books these days and does pretty good job.
I would think if your daughter started reading at 2, then BOB books at almost 4 are probably too easy and boring for her. She may need challenge as well as more substance. I say get different books, leave them lying around for a few weeks and see if she picks them up.
We too are starting piano with DS4. He will take private lessons but we signed him up for 8 lessons only. After that we should get a better idea if he is ready or not. I am worried that he is interested in it only because his older brother is starting piano too.
