Hi Springycurls
I work in a similar environment to your DH (govt, sensitive, demanding, niche, highly qualified), so may be able to bring you some perspective.
Jobs and ranks
In these sorts of work environments, you are employed for your brains and knowledge (even if it's not exactly what you qualified in). As such your opinions and input are respected whatever your age.
It's even possible, if the friend came in via Fast Stream, and your DH via a expert/skills job advert, that the friend could have ended up higher in rank. Yes, even if your DH mentored her - we respect the skills others bring to the role. Fast Streamers are very bright and rise very quickly through the ranks, but have to change role frequently, whilst specialists may prefer to stay in their area of interest. I know it can seem weird - I was once told off by my dad for showing 'insufficient respect' for and being teasing (cheeky) to an older man I worked with, (of the same rank) who he assumed must be my superior.
Age
The age thing is a non-issue in these circumstances. In my mid-twenties, most of those at the same rank as me were in their late thirties, forties, fifties. Why wouldn't I be friends with them?
And then, I suspect, both your DH and his friend are nerds. Nerds reach across the age and gender barriers anyway.
Gender In some areas of government, especially techy areas, men outnumber the women. Friendships across the genders are absolutely normal.
Until I had my first child I had almost no female friends, because I had studied and worked with almost only men. Thus my friends, including my best friends, are all men. My DH is absolutely happy and at ease with this. I even go on 'dates' with them, it's a joke between (all of) us. And yes, some of them I've had previous romances with, but all finished years ago (before DH) and not something I'd ever want to return to. Your DH had opportunity to be with this woman, but chose you.
Travelling together? I am always happy if there's a friendly face at my conferences and meetings. Someone I can chill with a bit instead of being on guard all the time. I can understand the messages they exchanged regarding the seminar and I would view them as entirely innocent.
"Not required that they go". In these kinds of jobs you rarely have a boss saying 'you must go to x seminar', it's usually a decision you can make yourself - and that decision is driven by professional development and need (whether info or networking). So he may not have a boss insisting, but it may be something he really should do anyway. It doesn't mean he secretly wants to rendez vous with this friend.
Sensitive work. You rightly suggest that the sensitivity of your DH's work might mean he sometimes needs to chat with someone who understands the situation, and to whom he can freely talk. Please don't take it personally. That's the nature of the job. It can be very hard to explain why something was frustrating and upsetting if you are unable to freely discuss the details. It can be as hard for us as it is for you.
Accessing his messages
Please tell me you only ransacked his personal phone (and that's bad enough). If you've gone into his work phone (you do mention work issues were being discussed) then both of you have a problem (him- security breach, you - sanity and the law).
Pet name That's the only thing I find a little unusual in this whole story. But it's not necessarily a worry. Depends what it is really. If it's obviously a lover-type name then I'd be more worried.
Politics We government types tend to talk a lot about politics I'm afraid, as it often has a big impact on our work, especially these days. I entirely agree with you that people can be married and have different political opinions (as long as you are in agreement on the underpinning ethical/moral values - i.e. you may not be able to agree on gay marriage in church, but you can agree that gay people shouldn't be persecuted).
I think you're in real danger of damaging your apparently good relationship with a lovely DH here. It seems to me like you are over-sensitive about being excluded from their world (through sensitivity, interest, or education), and possibly sensitive about being less highly qualified? I'm not sure that's the case, but I wondered. Please please take this opportunity to examine yourself and your reactions honestly.
Don't make assumptions about how he feels about you ('pleb')! My DH is highly qualified in his own field, we don't understand each other's fields at all (and like you, we can't discuss details). It just gives us a healthy respect for each other's expertise.
By not inviting her to your wedding you were being quite unpleasant towards your DH. Also, she was not to know that you excluded her on purpose (your DH might have said it was a numbers issue, for example), and a small gift and card seems a very kind gesture. At my wedding we had numerous opposite sex colleagues, friends, and exes.
If you contact her to tell her to back off, they would both, rightfully, be extremely upset with you. Why not make a genuine effort to get to know her, and her partner (just because they're not married doesn't mean it's not serious). Invite them both for dinner (the partner might be more on your wave-length, making conversation easier, then you can roll your eyes at each other when they go off on some nerdy tangent).
I'm afraid you don't understand their world and it will just make you look foolish if you continue on this path. If you really can't find some point on which you can connect, then step back, but let them have their friendship. There is nothing to suggest anything untoward going on here.