Hi Gemchloe, yes this does seem a bit extreem for your daughter, and only in reception class too. She is just getting used to school, and probably getting distracted during lessons. Could you ask that she be moved to another table, as I know, from my sons "chatty" behaviour at school, that it worked when he was moved.
You shouldnt have to worry about offending the teacher, its her job to teach. And if she is unable to cope with 5 year olds, then she cant be much of a teacher.
You do the best for your daughter. You could ask if you could sit in class, but it may make your daughter feel awkward, and you may not achieve much. But if you want to see how lessons are taught, then I think you should be able to do this.
Sometimes children act silly in class, as its their way of being accepted by other children. Again, my son did that too. And I had a word with his teacher, and him, and said to keep the chatting to playtimes.
Tell your daughter how bright and clever she is, and that she should show her teacher that too (kids love praise)
Being a parent is not easy huh! Good luck