@Gingerbeer I've read through this, and firstly, for you. I'm SO pleased your husband is with you, you must obviously be distraught to have discovered this.
Because of the Electoral Roll angle, it does seem that he has two settled homes and has for years, plus of course the fact that you've seen him and the other woman together coming out of the house.
To me, there are 3 options:
1) to say/do nothing
2)to tell your daughter what you've discovered
3)for you and/or your husband to confront the b., tell him what you know and ask him how he intends the rest of his life to play out.
Could be that your daughter, as Hetty wrote, knows about the situation, but I'd want clarification from him of this.
I'd certainly want to shield your daughter from unnecessary pain.
Again, all the best to you, I'm so sorry.
PS Years ago I went to the funeral of a man I knew through my work. And that was when his second family came to light. Two grieving widows, children from one of them...
I'd forgotten about this until just now.