In the Golden Compass, is Mrs. Coulter really lyra's mom?

Question

if she is, then why was she so mean to lyra?

Answer 1

Yes, she is really Lyra's mom. She is mean to Lyra earlier in the series simply because she wants the alethiometer.

Taken from wikipedia:

"Later in the series, Mrs. Coulter discovers the Church's true intentions: to kill Lyra. By then, she loved her daughter, so she kidnaps her and takes refuge in a cave. However, by that time, Lyra had long begun to hate and mistrust her.

Near the conclusion of The Amber Spyglass, Mrs. Coulter and Lord Asriel give their lives to kill the Regent Metatron and save their daughter (Lyra) so that she may safely fulfill the prophecy and free the multiverse from the oppression of The Authority."

Answer 2

Marisa Coulter, most often called Mrs. Coulter, (we do not learn her maiden name) was married to Edward Coulter. She then has an affair with Lord Asriel, and has his daughter, Lyra.