While it could be down to the early retcons to the original Overwatch (That even saw an Origins comic get cancelled), I think her Mommy Issues were maybe just a little misinterpreted.
When she replies sarcastically to people saying that "Ana would be so proud of you", people assume it's because she resents her mother and doesn't want to be anything like her. But she has an eye tattoo in tribute to her.
It's the opposite way around. Pharah idolised Overwatch and only ever wanted to join the team. But Ana never wanted Pharah to be a soldier, she wanted Pharah to live a normal life away from conflict. So Pharah is just acknowledging that she is fighting despite her mothers wishes.
It is clear though that Pharah is for sure closer to her father though, simply because he didn't pretend to be dead for the majority of her life.