This is the first time I have seen your posting and I have to say that your husband seems to totally lack self awareness and by seeing her privately again, after you have outlined the issue with him and he has moved to his mums, suggests to me that he is not acknowledging to himself that he is about to embark upon an affair. He has clearly handed her hope by saying he is at his Mums and if I was that woman, and clearly had no intent in that direction, I would be horrified at his situation and I would be on the phone, telling you so. I think she is holding out hopes that this is the start of something.
I had a close friendship with a male colleague for years, we regularly had lunch together but my husband and his wife knew, we were open and honest as we trusted our respective spouses and prioritised them. Had either of our spouses expressed concern, the relationship would have been down graded to work colleagues.
Rumours swirled about us, aggravated by the fact that his wife worked shifts and couldn't make some of the work related evening events we had and so she asked me to partner him as my hubby had no interest either. We didn't fancy each other, we enjoyed each others company and our partners knew that, we were honest and open and hide nothing. If you have nothing to be ashamed of, you don't need to hide it but the fact they were hiding it at work too, tells you that on some level, they knew it was not appropriate.
She is single, he is not, he is the one who must acknowledge his accountability and he has not. How can you trust him when for months he had not trusted you and has actually gone and seen her privately again, after you have told him how it makes you feel and what he risks to lose....he has poked the bear! He is in denial.
What likely comes next, in the fullness of time, is him having a fling with her....well if I am being accused of it anyway, I might as well just do it....in his head that will be your fault, you drove him to it.
Lets be honest, when you have been with a Partner for a long time, having someone else flirt with you is wonderful, if its harmless. But you cross that harmless line when you make secretive dates....that is not a platonic relationship, its taking it to the next stage, there is an intent there.