Wolfpack
Note: I haven’t read your backstory, so any references I might make about the affair you had are simply pulled out of the air. I don’t know if it was one or one hundred, physical or what.
These apps are listed under "entertainment" and are definitely not reliable. You could just as well choose random cards from a deck and the one with the higher one "wins".
I have written a bit here about poly’s. Both because of my experience ages ago as a law-enforcement officer and their usage in helping with difficult cases, but also because of the misconception too common about them.
First of all: a poly does not indicate if you are telling the truth or not. It indicates HONESTY. Big difference. Like if you truly believe 3+7=11 and were asked if 3+7=10 you would pass with a "no" and fail with a "yes". If you only remembered 5 affairs but your wife knew of 6 you would fail if asked "did you have six affairs" with no. It measures HONESTY, not the truth.
Second: Taking a poly needs to have a predefined result. Like... if you fail your wife should be ready to divorce because you aren’t HONEST to her and don’t trust her with the truth. Both things that prevent reconciliation. At the same time, if you pass your wife has to give you some credit and can’t go back to arguing that the affair started a month earlier, or if there was OW number 4 or whatever. It doesn’t close the door on more questions, but there should be a level of trust based on you having confirmed the truth to-date.
There is a possible second chance... If the result is that you fail but the scores not strong or clear you two could hash out the remaining issues and have a repeat in 2 months. But that would IMHO require the operator is clear on his doubts.
Third: You need to enter the test both believing the process. Save your money if you are going to question the result.
Are they reliable? Well... yes... Definitely not 100%, but I doubt a reasonably sane person can take a poly on issues that really matter to them and fool it. Most tests about the reliability are done with random groups of volunteers that face limited or none consequences when they say according to script "no" if asked if a fire engine is red. There are definitely other factors – sociopaths that don’t discern between right or wrong can pass, people can train to pass them, certain drugs can help pass them, the main problem though tends to be incompetent or unmotivated operators.
Fourth: The poly isn’t really the best place to ask questions that are to reveal new truths. You usually get 5 questions, and then one tends to be a rewording of one of the others. Ideally you want to know the truth of one hard question to use as a base-point.
Fifth: If the operator doesn’t spend some time with your wife alone asking her questions and what she needs to know, and then spends some time with you explaining terms and language used... find another one. For example: You want the term "sex" to be very clear because maybe you don’t see oral as real sex. When and if asked "have you had sex with anyone other than your wife since xx.xx.xx" you don’t want to pass by saying "no" if she KNOWS you had phone-sex or oral but you think it only refers to the actual classical act.
Sixth: The questions need to be factual. Like "did you have sex with OW" is answered with a yes or no and is quite factual: you did or you didn’t. "Did you love OW" is emotional and hard to change into fact. Not a good question.
With all this in mind:
Tell your wife that you both need to believe the result of the poly beforehand.
Tell her that you want to answer all her questions and that she can ask you ANYTHING, but the poly questions will be factual and not emotional.
Ask the operator how many questions and let your wife know.
You two agree on a grace-period for now where you can feel safe to share ANYTHING with her. No decision on the future will be made until after the poly.