WhatWas -
First, if you only want to hear responses from fellow wayward spouses, you can ask a mod to do that (you can start a thread in general titled MOD PLEASE and someone will get to you and you can ask that a stop sign be added to this thread). Having the stop sign is usually encouraged for newcomer WS, esp those who are experiencing the withdrawal from their limeraant affairs.
As to the "two Gottman trained" therapists? I'd bet a pretty large chunk of SI members (WS and BS) kind of shook their heads reading that. Many/most folks here have had at least one shitty therapist. Some have had several. So, I could "see" your 2-Gottman trained (I've seen 2 as well) and raise you a couple of CSATs (Certified Sex Addiction Therapists), and I doubt it would matter much.
There is at least one book that is pretty universally considered to be the immediate "go to" for a WS who is trying to come to terms with their crummy choices. That book is "How to Help Your Spouse Heal From Your Affair" by Linda MacDonald. It's a pretty short book, takes an afternoon to read. Get an electronic version & read it - TODAY (as in right now). Given you haven't told your BW about your LTA, a lot may not resonate. Read it anyhow (sounds like you have a good income, so you can afford the $10-15 even if you can't digest its contents - yet).
I don't see reason to rehash the STD issue. The risks here are basic science - the existence of the risk is not really open for debate IMO. The potentially lethal consequences to the mother of your children from your years' long sexual escapades with a sex worker outweigh ALL other factors here (and it doesn't matter if you used condoms, eg herpes can still be transmitted when using a condom, and you can be an asymptomatic carrier - it is not at all unusual) . Those risks outweigh even your wife's mental health issues.
I'm gonna echo what a lot of others said... there is not a doubt in my mind that your stripper girlfriend WILL tell your wife about your A, and it will not be done with an ounce of empathy or compassion for your wife or your kids.... or you. And I'm kind of curious what your "two Gottman trained" therapists think of that possibility. My WH had a 20+ yr A with a former GF, who never spent a day in jail, or traded sex for $ or many of the other poor character traits you describe. Yet that former GF (whom he'd known for close to 40 years at the time) told me. It happens ALL THE TIME, and from folks who - at least "on paper" - would seem to be far far far far far more trustworthy than your AP.
It is astounding how many WHs are so skillful at their cognitive dissonance to believe that their girlfriends would never tell their wives. Put simply, there is NO honor amongst thieves, and you and your AP are absolutely thieves. I'm confident you are very much aware of this.
One suggestion that came to mind (and I hope others will weigh in on this, as it may be brilliant or stupid) is to meet with your wife's mental health professional(s) and get their reading on the best way to become honest with your wife. This means accepting and deciding that you WILL disclose the A to your wife - and not letting anyone tell you not to. The goal is to figure out to do this in the most compassionate way, including making sure that a comprehensive support system is in place for her - even if it means having to hire 24hr/day live in care (which may be expensive, but given the $$ you've spent on your AP, perhaps its time to invest in your wife and not your affair). If your wife's mental state is as bad as you say, I assume she's got an IC and probably a psychiatrist. If not, why not? And if not, NOW is the time to get that all in place (again, even if you can't man up to tell her, you are foolish to not see that eventually your AP will do that for you).
I sure hope you don't close the door to SI bc of the response to this thread. Ask the mods for a stop sign and reread those from fellow wayward spouses (brave sir robin or Mrs Walloped come to mind as two WS who have posted on this thread). Get How To Help Your Spouse Heal - it focuses on what makes a successful rebuilder (and while she may be speaking in context of rebuilding the M, I think it's just as important to see it as rebuilding yourself - you are the one that is in need of some serious fixing). I just happened to read some of it again this AM, and one thing that resonates with your situation is that successful rebuilders learn how to set aside their feelings of shame in order to become empathetic to their BS. Sounds to me like a pretty good place to start.
ETA:
Another book you may find helpful is called Help.Her.Heal by Carol J Sheets. It's a workbook for a WS to build empathy. It's directed to sex addicts, but I think any WS can benefit.
And stay as far away as possible from Esther Perel and Mira Kirshenbaum. Most BSs (and some WS too) find their work to implicitly and explicitly blame the BS (even the "what made you vulnerable to an A" shit implies that there was something about the M that forced a WS to choose to betray and live a secret sexual life). That is not a good recipe for healing generally, and I believe could be more damaging to a BS with pre existing mental health issues.
Many Gottman folks are on that bandwagon too - the "what about the M or the BS made you vulnerable" bullshit. I think it takes time for a WS to get to the place where they can fully own their choice to lie. And from what I've seen, recognizing, accepting, and truly owning that NOTHING about your M or your BS made you choose to lie and to cheat is the only way to truly start changing yourself. You were vulnerable to cheating because you wanted to. You opened the door to that strip club all by yourself.
[This message edited by gmc94 at 11:24 AM, July 12th, 2020 (Sunday)]