Shari, I like your idea. But unlike a lot of the others, I do feel you shouldn't respond to this woman AT ALL.
Christians (hey, ALL religious people) come in many forms. Some are genuine, loving, generous and forgiving. Others are very much more old school. You also have to recognise that a small number of religious people are also a tad disturbed. It's fairly natural for some people who are disturbed to find solace in religion - there is a level of emotional security. But it doesn't automatically cure their underlying problems. Not many, and I say this as a Christian also; it's just that the more extreme people also tend to be more extreme in the manifestations of their faith. I'm speaking from experience here - I've spent the last seven years caught up in a friendship with a Christian woman who has serious mental problems (I do know, for she told me in great detail). I thought, by my trying to be there for her and listen to her, I was helping her learn to THINK rather than just take on board what she is told to think and believe.
In the end it backfired badly. It became too challenging for her to accept that life is not black and white, and the only way she could rid herself of the constant reminder that life is complex, was to purge herself of the person reminding her of this and trying to make her think. She takes advice from whoever she can get to agree with her viewpoint and is currently behaving very erratically. Many of us who have supported her now realise we enabled her, and her latest behaviour has alienated any last shreds of sympathy. This is a pity because she really needs support and balanced social contact.
Some religious people hide behind their religion and use it to justify their own extreme judgmentalism. If they didn't have religion they would find another excuse - politics, perhaps.
I also know others at my church, a very small number of whom each have their blind spots. If we disagree on something, I walk away rather than challenge something they hold too close to their hearts. What is the point of challenging what you know they cannot accept? It's Ross Greene again - Basket C. I love these people dearly, but we all have our faults, some of which we can accept and others we cannot.
My best friend grew up in an abusive family and married a violent man who was also a rapist. She finally broke free but whenever she's faced with a man who is drunk or loud, she just freezes. She is extremely intolerant of them. Where I will talk to them or stand up to them, she will walk away. When she hears of a woman in even a mildly abusive relationship, her advice is always to leave, immediately, and not even try to sort things out. Because for her, ALL abuse has become her abuse. But not all that appears to be abuse is incurable, or even abuse. Some things can be resolved.
But not this. Not at all. If you rub this woman's nose in it in any way, or even challenge, she will get even more righteously indignant and will HAVE to attack in order to continue to feel justified.
So don't reply, you are only adding fuel to her fire. Ignore her is the best option.
The majority of Christians (and other religious people) that I know are not like this. It's just unfortunate that when you find someone who is using Christianity (or any other religion) as a weapon to bludgeon people with, who quote scripture to justify a particularly narrow point of view, you need to tiptoe away quietly and not engage them. Because nothing you say will change them, it will only convince them that YOU are a danger and requiring cleansing. YOU then become a focus for their intense zeal. Speaking from experience - not pleasant.
And your original intent - totally blown away by major distraction.
Shari, if Arlene can reach out and support this father, she is doing a very unselfish thing. She could also be starting a chain of events which could lead to a lot of support all round. In our small community, for example, a mothers group set up a babysitting cooperative. It worked more formally, but the end results were greater than expected - not only was it much more possible to get babysitting when you needed it, but there was much more social interaction between parents (a lot of whom were lonely) and also the children. We got to compare our children more, watch them play together, and this helped those who had a child not functioning quite as well, to recognise it earlier and feel more confident about seeking help. Mothers with some degree of post-natal depression were more likely to get help because they realised, by comparison, that something was wrong and it wasn't their fault.
We have also a local Playgroup which for some years was chaired by a stay-at-home father. it was funny at times - his name was Chris, and he would get mail addressed to MS Chris *****. All the official people assumed that Playgroup couldn't be run by a bloke. But he was darned good at it and was an amazing support to all parents, including all the mothers. His kids are in high school now and the town still loves this family for what they do in the community. Playgroup did a lot for him and for the other stay-at-home dads.
If this father gets a chance to see how other parents manage, he might feel less overwhelmed. It has to help him socially, too, to be in a position to catch his breath.
I would point out, though - Arlene needs to be on the alert for two things:
1) She needs to be careful to not be simply taken advantage of; and
2) She doesn't want this bloke (or anybody else) to misconstrue her intentions.
If Arlene can adapt your suggestion to involve other at-home parents, it could be a big help to more than just this bloke.
Another addition to your suggestion - Arlene, instead of simply offering to mind the girl unconditionally, could suggest to the bloke that she could mind the girl in exchange for some yard work, or some handyman assistance, if it's in this bloke's capability. He would then feel more useful and less under obligation. He would also be less likely to misunderstand her intentions.
Shari, you are a decent, caring, loving person. Don't be blighted by contact with someone who is out of touch with humanity.
Marg