Op I hope you have not been influenced by any of the more pragmatic posters, what's happened to your sister is unbelievably cruel, and this starting a new, fantasic carreer at 50 which is going to make up for the past 30 years is absurd.
From the fact that they were together for so many years and this man never suggested marriage in itself tells you who he is.
There are many women as they age in long relationships that realise a quick service at the town hall can help protect them, I'm sure there must have been some conversation of this during their time together.
Even so, there have not been many splits I have known after so long whereby the male doesn't feel some responsibility towards a long standing partner and his four children, many men on here I'm sure would be disgusted with his behaviour. He's a very cruel partner, regardless of how 'happy' she appeared to be, she had no control, he planned the selling of her flat, totally premeditated, leaving her with nothing.
He has used her, and then abandoned her, this is total humiliation for her, I bet he was seeing this ow when he sold her flat and the fact he's kept up the pretenses till he bolted, and the way in which he bolted and told her whilst being on holiday shows he's a very cruel, conceited and sadistic person.
Please don't be swayed by op's, I think your sister has been abused badly by a covert narcissist, he had you all fooled, including your sister and his children.
The man has no heart, do whatever you need to do to help her survive, she must be very ill with it.
By rights he should fuck off and not force the sale of the house, give her time to set things in place to pay the mortgage and get back on her feet, he can have the flat.
What's the problem with this, his house will be left to HIS children at the end of the day when your sister dies, is it not enough that he's got to start a new life and abandonned them.
I've a feeling there is an ow who is pushing for a sale here, a demanding one, or in his eyes an ow that deserves one.
You mentioned parents, is there anyone who could loan within the family to buy him out, early inheritances etc. Thinking of ways to keep her in the house with the children.