Is your husband quite rich because, to be brutally honest, I wouldn't have chosen a man of 57 in my late thirties, even if he did look good for his age? When your husband is retired at 67 or so, she will be barely 50. If she stays she may well end up looking after some old man in carpet slippers who wants to stay home and watch television assuming he doesn't have a heart attack or stroke or other debilitating illness that is more likely in older people. And it does look like she made quite a concerted effort to worm her way into your family. I'd be incredibly annoyed about the babysitting by your daughter and the work experience offer. Frankly, in the circumstances, I'd be on the telephone to her husband but you may be a nicer person than I am. If she threw a bomb into my life I'd be throwing a bomb into hers.
I can't imagine what your husband is thinking of either. Imagine those two feral children with them 5 days a week at least. The mess, the toys, the arguments over food and homework, children complaining over anything grownup in the food like mushrooms or asparagus, holidays suitable for children, childish illnesses like chicken pox, norovirus outbreaks, getting up early in the morning to get them organised, the school run and so on. Then there's the screaming and biting eldest child. It is hardly going to be a cosy little love nest with that lot going on and his own children who now think less of dear old dad. That's if she has plans to leave her husband rather than denying everything and describing your husband as some lovesick old fool who has been bothering her. I think that's less likely though because if you were just looking for a quick fling you'd be looking for somebody young, good looking and hot, not some married late middle aged chap.
I know it will be a wrench to give up the family home. But it may be quite high maintenance and far more space than you need. You may find a lovely smaller place that suits you far better. I am betting that she won't come out of the marriage with a lot of equity and I suspect that she is not earning the sort of money you do so your husband may be feeling the pinch moneywise if they do move in together. He may be much less attractive with half his present assets.
Men say horrible things when they are behaving badly. They rewrite history to make themselves feel better because they would rather think of you as a nagging shrew rather than recognise themselves as unfaithful cheating scum. For some reason, they feel obliged to try to persuade their wives of this by sharing this with them as they leave.
Men sometimes do come back. Like many people by the time the man I thought was the love of my life was talking about trying again, I was just over it. There were nicer, better men out there. Looking back, I can't fathom the tears I cried over this not very special man and have nothing but relief that it stayed ended. You are much more likely to get a man back by taking a detached calm approach rather than doing the "pick me" dance. Desperate pleading and begging never works. But at the end of the day, after 35 years you shouldn't be having to play some cunning end game to win your husband back and I quite understand that you currently feel devastated.
You have the support of your family and your children. Your boss sounds very understanding and supportive. You have a good career and a good pension so you are much better placed than many of the women who find themselves in your situation. You sound like a very nice kind person and I am so sorry for what you are going through. You didn't deserve any of this.
Now being a somewhat shallow person myself, I always find a spruce up lifts my spirits. A new hairstyle or colour resisting the urge to chop it super short and dye it bright red (assuming you're not a redhead), some new make up, getting your teethw whitened and a few nice outfits can lift your spirits. Yes, I know you probably can't stop crying long enough to put on undereye concealer but you will get over this and you won't be sharing your house with the feral children.
I don't think anything I've said here would make the OW happy either so if she does read this, she should be ashamed of herself.