I spent half the movie screaming "YOU BITCH!" at my TV screen whenever Ellen Burstyn's character was on
Great actress. But her character was cold AF.

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"Did her mother ever get punished for what she did?"
I'd have to say she punished herself better than anyone else could have.
She was carrying forward what she was undoubtedly taught, and she was brought up to believe in a much stricter discipline. Julie's differences made her mother feel like a failure.
As for her husband, I think he passed away or something; it's not really clear but I don't get the impression he dumped her .. just think what a scandal THAT would have been!
GASP

Whatever happened to Julie's dad? Was he against what Iva Mae did to hurt Julie?

I just watched this movie and it was great, really showing how it was back then when a good girl got pregnant. Her mother reacted like most mothers would at that time in a small town. It probably killed her inside as much as it did Julie; that is why she continued to be a bitter, hard woman because of the hurt of going through that with Julie. But, you can see she softens when she gives Julie flowers for her wedding. That was a lot for her to do at that time.
So, she was being punished all those years, as a mother, I can see how much it would hurt. Her character is never developed, but if truth be known, she might would have loved to have had that grandbaby that Julie gave up.

Did her mother ever get punished for what she did?

Didn't she do a good job showing how the moral atmosphere was then? Doesn't it make you wonder what her childhood character would have been like. It just shows how the mores have changed over time. You know young people have been getting together since the dawn of time it's just how people accept it has changed.