Richard,
So today she came home, sat down with me and said what do I need to do to get you to believe me.
You need to ask her to go 'no contact' with the neighbour, as others have suggested. He has no reason to keep being in your house with your wife during the day when you are not there, it is having an adverse impact on your marriage and family, your wife knows this only too well, so why is the guy still coming over? You are well within your rights to say that you don't want a particular person in your home. And if your wife really wants to do what you need, tell her this is the biggest, most major thing you need.
You are monitoring WhatsApp intensively, wondering what contact she may be having with him, but if he is physically in your house, it leaves no digital trail, and, while nothing may be happening, they have the potential to do a damn sight more than just talk. So ask her to go no contact, and tell her that the guy is not to come into your house again. That nonsense has to end, because whether or not anything is going on, his continued presence is making you uncomfortable and corroding your marriage.
DarkHoleHeart said:
3. Place hidden camera outside your house, preferably watching entrances and surroundings. Can you see his house from your yard?
Secret cameras, if you can hide them, are certainly a good idea, on the back and front door of your home. However, why can't you go one better than this, and get security cameras fitted, which monitor the doors? Why hide them? Loads of people have them these days, for home security, and they will show who is coming and going. What can your wife say about you wanting to make the home more secure? There is no reasonable argument she can make for not fitting them. That will give you hard evidence of in and out traffic, plus a record of the times. That will help you to monitor whether or not NC is being maintained, because your neighbour won't be able to sneak in any more.
I think she planned to meet him on the Thursday as he was off work, and she was desperate for me not to come home from work during the day when I said I needed to sort my head out.
How did you know he was off work on the Thursday? How did your wife show her desperation for you not to come home? That seems like odd behaviour by her, particularly when she is under suspicion. However, if you have a way to know when he is going to be off work, those are clearly days when you need to be coming home unexpectedly. And, obviously, any other times when your wife makes it clear she doesn't want you around.
Have you told the neighbour that you do not want him coming into your home? You have every right to do that, and you can tell him that his relationship with your wife is putting a strain on the marriage, so it has to stop. He has a wife and kid(s), so he doesn't need yours as well.
Does his wife work, or is she home during the day? If she is home during the day, it cuts out the opportunity for his place to be used as a location for 'contact'. If something was going on - which as we keep saying is nowhere near having been proven - it could explain why your house has been the main base of operations. Like I say though, nothing is proven.
If you ask her to go NC, and you find she has broken it, then - without telling her - I think you should go and talk to his wife, and tell her that you are concerned about the relationship between your wife and her husband becoming inappropriate. I know that is a 'big' step, and we have to think carefully before we rock anyone's world, but even if she thinks you are crazy, she is bound to mention it to her husband, and the only conclusion they can come to is that it will be better for him to stay away from the crazy couple across the street/next door, because they are just trouble, which effectively solves your problem. However, I would save this as a 'zero option', to only do as an extreme measure if NC is broken, or the guy keeps coming to your house after you have made it clear you don't want him there.
Having said all of this, I have to repeat what so many others have said, which is that you have basically no evidence of anything going on, beyond the issue of your wife and the guy being on WhatsApp at the same time.
What is really bothering you is the uncertainty.
Richard, I'm not sure where you are (and no need to say!), but for the cost of a few hundred dollars/pounds/euros, you can get yourself a few VARs for the house and her car, plus a couple of motion-activated cameras disguised as digital clocks, and you will have much better evidence to analyse than possibly co-incidental appearances on WhatsApp, which do not tell you the content of any messaging that was done, or even if they are contacting each other, despite being online at the same time.
As DarkHoleHeart says, you can download software called Dr. Fone, which can help recover deleted texts, messages, etc, but if you do not feel technically savvy enough to do it, you can get a local computer or phone store to do it for you. Just ask around, it's a straightforward process, people are always deleting stuff they wanted to keep, and they need it recovered.
Honestly, by spending some money on a few VARs, a couple of little cameras, and either Dr Fone or getting a local business to recover deleted stuff from your wife's phone, you can end a lot of the uncertainty that is preying on your mind. I really think it would be a good investment, don't you?