I am sorry that this is happening to you. I do not have the impression that you are about to decide not to pursue this, but if you do decide to stop, for whatever reason or none, that is your right as well and I would support you in that. You must look after yourself in the middle of all of this.
I once heard, at a panel discussion, someone asked why the panel member endures the equivalent to the type of discussion you are having with your management, herself. She answered that she endures the pain for future women and not for herself. This is honourable but it is not an obligation. Do what you can and seek support for yourself, here and from your husband who sounds as if he has a good sense of humour and perspective.
I am not expert in the law, but I agree that if you were to resign you would have a case for constructive dismissal, should you wish to pursue this, and that documenting every conversation, including that one in which someone mentioned a cover story is what you need to do. It is possible to make notes during a meeting, show them to the person in the meeting, and then email them around there and then, or, yes, bring a union rep, third party, or someone from HR to witness the conversations.
From the perspective of your organisation, your managers may believe that losing you, even with a constructive dismissal case, risk to the organisation's reputation and all, to be the lesser loss than losing him. Depending on the short- and long-term goals of the organisation, they may even be right, tragic as it is. I would not run an organisation along such lines, and I do not run a organisation. I once heard corporations described as people without souls.
You are being courageous 