Let me preface what I'm about to say by telling you that I used to feel the same things you are describing when I was with my ex. I truly sympathize with feelings of fear and insecurity and having a partner who sometimes doesn't know where the line should be drawn does not help. It's a lot to handle and I can't imagine being pregnant while dealing with those emotions.

I'm really sorry for all of the pain you've felt and for the position you and your dh are in right now.
My ex made a lot of similar mistakes - he never physically strayed from our relationship but he sometimes overstepped the boundaries with female friends and, I'm sure, liked the extra bit of attention from them. I won't go into details but there was one night in particular in the first few months of dating that started the cycle of mistrust and overreaction for us. He knew he was in territory he shouldn't have been and I was extremely hurt. I felt betrayed. From that point on, he promised he would watch his boundaries and for awhile, he did. However, he would lie about things, and sometimes he genuinely thought something wasn't a big deal and so he just refrained from telling me because he knew it would upset me. Sometimes he probably knew he was overstepping. Either way, it was always a fight - in my mind, I always thought, "If it was innocent/if nothing is going on/if you didn't mean anything by it, why would you lie about it? Why cover up what doesn't need to be covered up?" And in his mind, I think there was a combination of, "I said I was sorry and you still don't trust me. I'm not even going to tell you about this because I know it wasn't the way you'll take it and it isn't worth the fight." and "I know I shouldn't have done that, but I'm going to try harder next time so I don't think I need to bring it up." Additionally, when I would lose my temper when he did tell me, it didn't really send the message that I was "safe" to share things with.
He had bad boundaries and didn't understand where I was coming from. I was insecure and that insecurity would intensify with every incident and I would get more and more paranoid and my reactions would be more and more intense. It was a terrible, awful cycle to be in. Neither of us knew how to communicate what we needed from each other and neither of us knew how to come to a healthy solution that didn't make him feel like he was boxed in and set up for failure no matter what he did (because really, being mad at him when some other girl would say or do something wasn't fair - if he responded positively to it, that's reason to be upset with him but he couldn't control what other women said or did any more than I could, and truthfully I forgot that sometimes, in the heat of the moment) but that also didn't neglect my feelings and neglect the healthy boundaries that should exist within a committed relationship or marriage.
What I'm reading from you is that when he was making progress, you 'trusted' him but only as long as no women were around. While I fully understand that standpoint and fully agree that trust needs to be earned back, you can't get rid of every other woman in the world. There are people who can and will do things that threaten those boundaries and you can't stop them. You can't expect him to, either. If she showed up, he doesn't really have the power to make her go back home, you know? What he CAN do is stand his ground, refuse to engage it and let her know clearly where the boundary is and remove himself from the situation if possible. And trust me, I remember that feeling of being totally shaken by someone else intruding on our relationship or our commitments to each other in some way. Your stomach drops and your heart races and it's just terrible. What I learned from that relationship, though, is that I can't hold someone responsible for something that they couldn't control and that I can't trust someone because there just happen to be no threats - I need to be able to trust that they will do their honest to God best to keep themselves from being in a position they shouldn't be in AND trust that they will respond appropriately if someone else infringes on that.
I'm not sure what the details are with your dh's work and whether or not he would have been allowed to just leave. I don't think it sounds like he handled it as well as he maybe could have and if he agreed to call you about that sort of thing as a way of being accountable, he should have fulfilled what he said he would do. I would give him credit for not having a drink with her and for telling you about the incident. That DOES sound like progress for him.

And for what it's worth, as an outside party, you sound like you've been on edge about this woman since she was hired - do you think there's a chance you're maybe seeing threats that aren't necessarily there but in your mind, you've convinced yourself that they are?
Please don't think that I'm saying we should be happy about hearing about their mistakes and we should trust blindly and we should be an everlasting fountain of patience and forgiveness. We are human, too, and we are entitled to our own emotions.

Something like, "Thank you for telling me about tonight. I'm not happy that she showed up that way and she was asking you to drink with her; it makes me feel afraid and vulnerable. I'm also a little hurt that you didn't call me then and in the future, I would feel a lot better hearing from you the way we discussed. I do appreciate that you shared this with me, though, and I appreciate that you declined to have a drink with her." might get everything across. I do realize that's pretty composed for the level of emotion you were probably feeling and so if you need to say, "I want to respond in a way that helps us build instead of tear down, but I am feeling a lot of big emotions right now. I need to take some time to myself to process all of this. Can we agree to talk about it later?" I realize speaking that way is the last thing you want to do when you're feeling all of that, but taking the time to control your response really can do wonders for your communication and for your relationship should you want to make it work. Honestly, he probably thought he did a great job by being straightforward with you about it and for saying no to the drink. That doesn't mean there's no room for improvement because there is, but it would be a lot better for your relationship and your sanity if you were to take the victories as they come, expect "2 steps forward and 1 step back" as he progresses and process your emotions separately from his progress. I know they're intertwined, but your insecurities, your issues stem from something before him, most likely. His need for validation stems from something before you, most likely. Individual counselling may help you both address those issues, too.
If you can address the root issues, you can process and move on. It's the difference between putting a bandaid on the symptoms of those issues and really, truly healing them.
Additionally, he needs to continue getting used to enforcing boundaries in a new way. He needs to continue to be strong in those boundaries. He needs to continue to be accountable to you. You need to become a safe place for him to come. Validate him where it's deserved. Don't let the emotions and fears control you and how you respond.
That was really the tip of the iceberg when it comes to my ex and I and needless to say we haven't been together for a long time. It was my decision to leave, in the end. A lot of what I've learned, I learned on my own, after the fact, and have worked on it further with my fiance, with whom I have a very wonderful and healthy relationship.

We both came from unhealthy previous relationships and we both had many issues to work through together, but we have truly come a long way and we have truly overcome a lot of deep hurts and issues. It has taken a lot of effort and communication and a lot of prayer, but we have truly healed from a lot. It is my belief that anything is fixable as long as both parties are willing to work hard. What that looks like for every couple is different.