It was the "me and my friend" that the kids objected to. The teacher's response was that another teacher made the worksheet.

Another example is" Mary wears a pair of socks. This teacher says socks is the direct object. As in Mary wears socks and "a pair" modifies socks. Experts? Is this true? DD is not confident in this teacher.

And "She is older than me" is correct rather than "She is older than I". (Internet search says this is controversial)