Is Elizabeth embarrassed by her mother?

Yes, in Chapter Nine, Elizabeth asks that her mother be summoned to visit Jane, and Bingley complies. When Mrs. Bennet arrives, she is pleased to see that Jane will eventually recover but still ill enough to remain at Netherfield (and in proximity to Mr. Bingley). Mrs. Bennet lacks subtlety and her intentions become quite clear to everyone at Netherfield. She is also openly rude to Mr. Darcy. Elizabeth is embarrassed by her mother's behavior and pleased when Mrs. Bennet departs.