It's not up to the church to judge, it's up to God. Your sins are between you and God. The church can ask her not to come back, but even that would be wrong if you ask me. God is about forgiveness and compassion. The church should be striving to be more like God not more like humans.
Here's a little story, maybe it will change your mind.
At our church we had a guy that had been in prison for some bad things join us. When people found out they went crazy. Our pastor tried to explain that we should be welcoming, especially if we believe someone is a sinner, if they come to us. People eventually drove him away anyway and I thought that was very sad. You could see in his eyes that he was so sorry for his crimes and wanted forgiveness and people just wouldn't give it to him. I think if he's truly repentant that God will welcome him though and I hope to see him in heaven someday and maybe then he can smile again.
The guy had gone to prison. He was punished already, and he was sorry for his sins. If it was made clear to the woman that she should stop the sexual relationship, she should have stopped. Every church is different. It would have been better if the woman was more discreet, but if she attends a church that doesn't approve sex outside of marriage, they had every right to have her leave. How can they teach their own children not to have sex outside of marriage if there is a woman who is doing the same thing and is not sorry for it?
I don't agree with the tenets of that particular church, but once it is known what the church stands for, you as a congregant are obligated to follow the rules.