Bugsy, I'm so sorry you are in this awful limbo and can see why you don't want to chuck your husband out, even if you feel like it. Young children complicate things no end. As you say, you know your husband has to work with this woman, anyway, so he can't stop seeing her.
The sixty million dollar question is how can he prove that there is nothing going on between them? And FWIW I think you do need proof. After all this deception, an explicit text message just before your holiday to cap it all, you deserve more than his assurances that nothing is going on.
So how do you get that proof? no wonder you mention hiring a private detective. If you really are thinking along those lines what are your views on meeting this woman? I am sure you must have mulled it over. I can speak from some experience here - years ago I broke up with a serious boyfriend but some months later he wanted to get back together. I knew his curent girlfriend was still on the domestic scene, despite his protestations. I let this situation go on for a few weeks, but nothing was resolved. My boyfriend was trying to let her down gently, but hadn't quite got round to telling her to leave. I gave him an ultimatum. He didn't meet it. I knew my boyfriend had great power to hurt me, so I planned an all or nothing meeting. I arranged to meet him in a public place. I then contacted the other girl and arranged to meet her too - same place, 20 minutes after my boyfriend was due to arrive. I didn't tell either of them that I had invited the other. When my boyfriend arrived, I asked him again if he really wanted me back. He said yes. Then his girlfriend arrived. Both parties were shocked and totally angry with me of course. I was beyond caring - I just felt we all needed to know where we stood. I asked my boyfriend to tell the girl what he had just told me. He did and the girl moved out of his home the next day.
I am sure the girl hated me, but I might have saved her from a long drawn out and confusing time. My boyfriend and I went on to have a good relationship once he had got over his anger with me and I had built up my trust in him again. He kept to his word and was never to my knowledge unfaithful. But it took a year for us to get back on an even keel.
In hindsight arranging that meeting was a great thing for me to do. I had given my boyfriend all the chances I could to prove his commitment to me. He didn't take them. I knew his dithering was making the other girl miserable too. I needed to hear my boyfriend say to this girl that he wanted me. I felt I had nothing to lose in the end.
This type of showdown is probaly not for you - I just wanted to show you that sometimes it can work. Of course I had no children too, and the girl and my boyfriend did not work together.But I wonder if some sort of meeting might work for you? even meeting up with this woman alone? From your messages it sounds as if she is very aware or your anger and knows that you and your husband are having a very difficult time. Why are she and your dh being so insensitive?
Alternatively, can you ask your husband to find another job? Could he start looking for work with another company? even if there is some financial loss, what it this against your peace of mind and your future together? People leave jobs all the time for personal reasons. FWIW I really think you have a total right to insist this now and that might be your best option.