Mrs Mooney
You can't hide anything from Mom. Not if your mom is Mrs Mooney. As readers, we don't even find out the secret until she does: the first time we get wind of an affair between Polly and Mr Doran is when Mrs Mooney "noticed that something was going on" (The Boarding House.4). We should have known from the start that she'd be in control of things, this woman who got a divorce from her drunk husband when you couldn't just like a divorce lawyer's Facebook page and annul your holy matrimony. Oh, did we forget to mention that she ran a butcher's shop? Yeah, don't mess with this mom.
It's not like Mrs Mooney cuts to the chase, though. At first, "she watched the pair and kept her own counsel" (that means she didn't say anything to anyone). This strategy had exactly the effect she intended because it started to get to Polly and Mr Doran. They knew she knew about them, and they knew she would pounce, they just didn't know when. It's got all the suspense of a horror flick, but it's supposed to be a love story.
Let's take sides for a minute and give Mrs Mooney credit for being not only cool, but also calculating. Unlike Mrs Kearney in "A Mother," Mrs Mooney doesn't ever lose her temper. Unlike Eveline's father, Mrs Mooney doesn't freak out as soon as she finds out about an affair. This is a rare display of calm in the face of adversity for Dubliners.
Parental Control
Does this make her a good parent, though? Well, not really. Like those other two parents, Mrs Mooney is out to protect numero uno. She actually wants Mr Doran to marry Polly because she'd been thinking of sending Polly back to typing school anyway, and because she knows that it's probably a better marriage than Polly would get otherwise.
If Mr Doran thinks that Polly's "disreputable father and […] her mother's boarding house" will count against Polly's value as a wife, you better believe that Mrs Mooney knows this, too. Before she talks, she looks at herself in the mirror and thinks "of some mothers she knew who could not get their daughters off their hands" (The Boarding House.10).
And check out how Mrs Mooney isn't even nervous when she confronts Polly and then Mr Doran. She plans the whole thing out so she has time to sit in her rocking chair before she talks to Polly and then catch mass after she talks to Mr Doran.
Her cool, calm, collected demeanor helps us see through her argument that the whole thing is about saving her daughter's honor. The real thing she's interested in is getting Polly hitched and off her hands. The fact that she uses the phrase, "sure was she would win" two separate times pretty much gives it away that Mrs Mooney doesn't want to resolve a matter or have a conversation or look out for Polly's well-being: she wants to triumph.
The real question that we should ask is whether, at the end of the story, there's really much change between the Mrs Mooney of the butcher shop and the Mrs Mooney who takes down Mr Doran. Even though Joyce doesn't actually reveal the outcome of the argument, we're talking about a former butcher here. What would you do in the situation? Yeah, that's what we thought.