Go with your gut. Though this is the 21st century and work places have been co-ed for a very long time.  

My BIL1's then fiancé and ultimately his bovine bride demanded that he not even look at females and not to say a word to them. She even tried to enforce that when he was visiting his sister (my DW).   He was in the Service at that time and stationed across the country from his home town. He would visit us fairly regularly as we were a relatively short bus-ride away in a neighboring state. We had great visits with BIL1.  He is a big C&W music fan and there are a number of great music venues in the city we lived in when he would visit.  The dumb ass would literally turn away from any young woman.  There are several dance halls in and around town where some very good artists performed.  These are notable historic venues.  Honky Tonks, etc...

I was mortified by his pathetic behavior.  Several young women would ask him to dance and he literally would ignore them and turn his back to them. So, I danced with them and we had a great time.  That did not bother my DW one bit.

I would be wary of over playing this hand.  If he is cheating, fry his ass, take him for everything, and put his ass living under the local overpass in a refrigerator box.

However, just because there are women at his work place on teams he is part of does not mean he is cheating.  I have led a number of teams over the years on extended international and domestic business trips that included several women.  All professional.

I did have a Sr leader I was matrixed to who had a problem fishing off of the company pier with young professional women.  He was married with infant twins at that time I was pulled into an invetigation on his behaviors.  Ultimately he got shit canned and some of the young women who would leave his hotel room doing the walk of shame back to their room to get ready for meetings were released as well.

It could destabilize your marriage and your families financial security if you are not careful.  If he is doing nothing untoward and you are being unreasonable in your position I can see how he would think it to be much easier to not share that he is on a travel team that includes a woman if this has been an  ongoing issue.  Withholding that fact is certainly a stupid choice on his part.  However, how much pressure have you applied on this issue during his career and for how long?

That may be relevant.

I hope it all settles out as you prefer.

Take care of you.

Did something happen, is something happening.. will something happen? IDK

Are they in what some call "work wife/husband" dynamic.? maybe? where it's platonic, but they rely on each other emotionally? 

At this point, I think you either need to leave.. or go to couple's counseling.  I don't think you can stay with the current dynamic.

Because, why would you want to stay with someone who has such a negative opinion of you? he says he cant tell you things because you always are angry! I mean.. are you? or are you just frustrated by his inability to grow a backbone with everyone else BUT you.

I mean forbid he deprive his children, go against his ex, deny his time to his coworker.. but fight with you constantly? yep.. hide things from you? yep.

Maybe it's the over time wearing down of disagreements over all his kid's activities... maybe he is just not a nice dude

But, like the situation with his kid's sports.. you are raw to it... and I don't think you are crazy for thinking there is more fire than smoke here.  it sounds suspicious as hell.  

I mean.. yeah.. men and women work together all the time.. travel together.. I do it/. but I would never try to lie to my husband or intentionally omit things about it.. THAT is the issue... NOT the travel issue.. it's a intentional effort to mislead you that is the problem.. and this is not new... I think he does it re his kids too.

This can happen at any job.   No job is as important as a marrage.  And if he did it once [ ST boards. Assuming he was marrage before,  you]. He has practice,  and practice makes perfect.  Second time better in hiding his affairs.  Another thing about second marriages.   Is SO,  did it before, he had the [ in moral to do this before. ]You will never fully trust them ever 

You can't get over it because he didn't make any effort to make amends to you. He deflected the blame on to you for "getting angry" and then distracted you with arguments over other issues.

I lived in a state of hyper vigilance for months and months when I suspected my XH's affair. It was pure misery. I agree with ESMOD that for your own good, you need to either leave or go to therapy together. Living like this is just not sustainable and he's proved that he can't "do the work" on his own. He honestly sounds like a nightmare all around, and his behavior is incredibly suspicious.

Listen to your "inner voice" - I think it is trying to tell you something. There is a reason that you can't let this go. Hour long phone calls seem like way more than work. Is he doing anything else out of the norm? When my ex was fooling around on me I knew something was going on, but wasn't sure what. Once I discovered the truth, so many little things fell into place. But the biggest thing I ignored was the feeling that something was off. There were many things it could have been, and I looked to those first - while ignoring the biggest one of all.

This is not a good way to live. I would suggest either therapy or a private investigator. I know that sounds a bit out there, but at least you would know for sure. Sorry you are having to deal with this, especially at the holidays.

Ok, from the hip, a good relationship depends on three pillars, trust, communication,  and respect. If one is missing,  the rest all crumbles. Yes, love is important but it's a bonus. If you have love but not all three others, you have a situation that won't withstand the test of time. 

FWIW, I have worked long distance with colleagues and colleagues who became friends and never had  an hour long phone call. If it's a regular occurrence then there is either a clear lack of training (yes, it happens) and needs to be addressed to bring her up to speed or she's not in the right job. Your DH should address this with her superior. It's not his job to cover othe people's lack of experience/competence. 

Does he work from home ever? Could you tape a recording device on the bottom of his chair? 

Im not saying your husband is cheating BUT this is one reason why traditional families kept one or both of the spouses at home 

The temptation is real and we spend more of our day with our coworkers than our actual partners 

Line the kitchen table with classified ads for work from home positions if he seems to be struggling managing a coed workplace

Some of these men are only as faithful as the options right in front of them. 
 

Maybe seek some couples and marital therapy for you both.