Polygraphs are good only for carefully worded yes/no questions. You already know he's used prostitutes 3 times, and you already know he may be lying. Does it make a difference if he's used them 4 - 10 - 25 - 100 - 1,000 times? For a poly to be useful, you have to know where the lines that will drive your decision are. It will take time for you to determine your boundaries.
When that time comes, maybe a poly will be useful; maybe not. An example: My W came clean on d-day. I got more info over time (I did a lot of interrogating), but everything she said was consistent with what she told me on d-day, and I rejected the advice to do a poly.
Perhaps I could have gotten a poly shortly after d-day. By the time I was ready to decide to commit to R, I thought I was more sensitive to her truthfulness than any poly examiner would be. Sure, I had accepted lies during the A. After her A, though, I'm sure I recalibrated to her non-verbals well enough to distinguish truth from fiction. I think most of us can be better at detecting lies than any poly can.
My suggestion is to hold off on any poly until you know which questions are crucial to your decision. If those questions can be answered yes/no, maybe the poly will help.
Below are some of my recos for living with your H while you decide what to do. Note that a lot is stuff I did that worked for me. I'm sharing only to give you some options. Feel free to copy, adjust, or ignore my recos. What counts is what will work for you.
Read Not "Just Friends", especially the parts on making decisions and recovering.
Feel your feelings. Let them flow. Know your wants, and get them fulfilled to the best of your ability. If you want sex, initiate or accept your H's invitation. If you don't want sex, refuse. If you think you want it but it's not working out, stop - if that leaves you H unsatisfied, so be it. If you want sex but not the way your H is doing it, let him know and ask for what you want.
IOW, ask your H for what you want. If he's unwilling, negotiate a solution, knowing that the solution might be to split.
If you want to be held, ask. If you don't want him to touch you and he approaches, send him away.
If you want to cook, cook. If you want to take care of your meal but not his, so be it.
Test your H as much as you can. If you have lots of common ground and shared desires, maybe R is a good idea. If you don't find common ground, you may not be a good fit for each other, and D might look pretty attractive.
Accept your feelings and thoughts as they occur. I was able to form an executive in my head, and my executive made me ride the waves without beating up on myself or my W. I think that helped me a lot, and I recommend doing that if you can. I certainly told my W when I was angry, but I found much greater release in yelling, 'I'm furious at you for _____' than from calling her names or otherwise attacking her.
I took time pressure off myself. I was quite a bit older than you, I think, on d-day, but even so I knew I was likely to live a long time - I wasn't going to let normal emotional reactions make a decision that was going to affect decades of my life. I kept myself focused on figuring out what I wanted and figuring out if it was attainable without requiring more effort than I thought it was worth.
I dug into myself. I accepted that I wanted to be loved and desired (despite my shortcomings). I accepted that finding out if my W loved and desired me required taking the risk of finding out she didn't. I asked the big relationship questions, know that just one wrong answer could make me end our M.
IOW, you need to commit to make mindful choices about what is best for you. It takes effort and courage. Your posts indicate you have the energy and courage that's necessary to thrive after being betrayed. You've started out by asking the right questions.
Your decision can come naturally, and it's best if you let it form itself organically. I think in terms of head (logic), heart (desires & other emotions), and gut (intuition). If you let them, eventually they'll align, and you'll know what you will do. My strong reco is to let that happen, not force it.
And you need to commit time. Surviving and thriving takes a lot more time than anyone thinks it should. If you choose D, think decision time plus 1-2 years for recovery. If you choose R, think decision time plus 2-5 years to recover and R. You won't always feel as awful as you do now, but recovery is slow. At first you feel good for so short a time that you won't recognize it - but in all likelihood, you'll start feeling good when you make your decision - assuming, of course, that you don't decide too early.
Although your decision is best made while putting yourself first, if you want R, you need to attend to your requirements for R, and you need to find out if your H will commit to meeting them.
R takes courage and commitment from your H, too.
But don't waste your energy thinking about him unless R is a possibility. If this is a deal breaker, recognize that, and save prevent heartache for yourself.
I know it's easy to spend a lot of energy thinking about your WS. It's a trap. Think about yourself and your wants first. Do you really want to grow old with him if he meets certain requirements? Or are you done? If you're done, he's just an obstacle to the D you want.
If R is on the table, what he has done is of less importance than what you both will do to rebuild a marriage that will serve you both well.
Of course he gets away with his infidelity ... oral sex with condoms for pay? Knowing he's fucking up with fucking? Getting arrested? Possibly losing you? Oh, wow! What a great life....
You heal you. Process that pain of betrayal out of your body.
He heals him. He has to change himself from betrayer to good partner. He will probably need a good IC for an extended period to do that.
Together you build a new M. Or not.