workJack:
It's very hard to suggest what next without knowing how strong a reader your DD is.
I'm just a parent, but I think the question I'd be interested to ask is what does the teacher think about your DD's reading out loud skills - is it full of expression? Is it fluent? Would she benefit from you and your DD discussing things like what might happen next in the story, which character she likes/ dislikes, meanings of words, etc....?
This is a really tricky stage and both DDs (although with DD1 it was late Y3/ early Y4 because she was a struggling reader, especially when reading out loud) - but our solution was to share nightly reading. We didn't ignore the school guided reading selections, but maybe gave them 2/3 nights attention out of the 7 and the rest of the time we read things totally off the school plan.
So we would each read a page of Charlotte's Web, Paddington, Charlie and the chocolate factory, etc... basically old favourites so Mum & Dad could relive their childhood! For DD1 at this age - a lot of this was too much to ask - so I would select a short, easy to read paragraph or maybe have her try a difficult sentence, but would do the bulk of the reading myself. Gradually over time, the balance shifted, but I found that if I was reading to them a bit more than they were reading to me - they felt they were on to a good thing, they enjoyed this quiet time after bath & before bed and I enjoyed sharing some of my favourite stories with them.
HTH
PS listening to someone read a book is also important - I think it gives you an appreciation for English - it's rhythms, forms of expression, joy in puns, etc.... we tackled this in two ways - tv shows (CBeebies Bedtime stories/ specials like the Gruffalo at Christmas/ Jackanory/ Bookaboo (I'm a bit out of date so some of these may no longer be running) - and CDs of chidlren's stories. The Harry Potter books read by Stephen Fry for instance are brilliant on long journeys.