I'm curious so I hope it's okay if I ask, what type of work does your husband do? Is he a trucker (18-wheeler type)?
Magdlyn does make some good points and I think the one that sticks with me most is how difficult his work schedule is. Heck, even if he was single with nothing to do at home. 16-20 hours a day with no days off for 3-9 weeks? I'm surprised he doesn't just sleep for the whole week he has off. I guess that does make counseling tough to benefit from, heck it makes it hard for him to maintain (let alone improve) any relationships at all by any means, and yet he's (essentially) got two wives to husband and five kids to father. I guess it's no wonder he doesn't bother putting much work into improving things with his ex. All his energy is pouring into his work. Even his emotional energy must be a sorely depleted.
It seems to me that the main thing you'd like to see improved is that you'd like him to have more desire for his ex, also for the whole family to be happier but for that we need the specifics of what's making everyone unhappy. I sense unhappiness coming from his ex because she'd like him to desire her more, and I sense unhappiness coming from him because to him it's a hassle to have any romantic (or even platonic?) relationship with her at all. And maybe you're (somewhat) unhappy because you see that dynamic between him and her and it disappoints you that they're not happier. (Are the kids happy enough in your opinion?)
As I said, the main problem seems to boil down to the unease in the relationship between your husband and his ex. We have determined that her chemistry needs medication (for her emotional well-being and so she can be nice to her loved ones), and she is now on medication. How helpful is the medication so far? Does it need any tinkering (with perscription type and dosage)? Is she doing better for her kids? Is she doing better for your husband? Are these improvements sufficient to make the kids happy? Are they sufficient to put your husband's trust issues on the mend? Is everyone's happiness improved enough to grant you contentment? If not, is it continuing to improve?
Is there anything amiss besides her chemistry/medication issues? Are there specific things she ever did to wound your husband that she could make right? Do the children need any specific kind of restitution from her?
We can certainly advise you on this thread; I believe we have, and I believe we'll continue to do so as long as you still desire some added advice from us. Let's just say that the more specific information we have, the better (and more helpful) our advice can become. Which is why I ask the questions I ask, and in general I encourage you to share as much information as you feel you can, even if it means lengthy posts and you feel like it's overshare. You never know when some detail on your end could germinate an idea on our end. Plus just talking about the problems may give you some more ideas.
I have to perceive your situation as challenging to say the least, but that doesn't mean I think you should just throw up your hands and quit. Some situations that would suck for one person work just fine for another person. I guess my objective is to see you get to a place where you feel contented with your family relationships and where they're headed. If by any means that can be accomplished, then let's put our heads together and figure out how to do it.
Just as an aside, how well are you and "the ex" getting along? Are the two of you happy/contented with each other at least? If not, what needs to improve?
It sounds to me like on average, both of you are okay with your husband's long absences. (Are the kids also okay with it?) If so, then I'll not even worry about it. Is the hard work schedule doing him under? Is he frustrated with the family time it costs him? Does he need a job/career change for his own sake, or can he (continue to) cope with it? I know he's tried to get off once every three weeks, but for now let's assume that'll never happen and confirm that everyone in the family can at least live with it. I know you said you've found it to be a bit much lately. Do you think things will settle back to a 4-5 week work block soon? Do you need your husband to seek a new line of work?
Bottom line: what's the minimum of things that need to improve before everyone in your family can be satisfactorily happy? Let's draw up a description of that (perhaps in list format), and go from there.
Love means never having to say, "Put down that meat cleaver!"