This sounds a dreadful situation and you are right to discuss it with your children, and then to contact your doctor. There was a situation like this some years ago at my church when a very respectable married man, much younger than your husband, pillar of the church,became obsessed with a happily married woman. She disregarded his advances so to impress her he raised a considerable amount of money for the charitable work she was doing, only it wasn't fundraising, it was theft from the accountancy firm he worked for.
The sooner you can get your husband's obsession recognised as an illness the better; I am sure there is a medical reason for this change in his behaviour. I would not discuss it with the woman concerned until you have had a medical assessment of your husband, and you must pester for this.
It doesn't seem as though your husband is receiving any encouragement from this woman, and I imagine she would be alarmed if she realised the extent of his obsession.
It may be a good idea to consult a solicitor and register your concerns about the situation.