I read it.
Have you heard of Occam's razor ? If not - Google it. Basically, it says the simplest explanation for something is usually the correct one.
I'm so sorry - there is no nice way to break this to you.
Your wife is having a physical affair with this guy.
No one carries a single condom around with them unless they have an expectation that they are going to have sex.
99 times out of a 100, that is the explanation. So let's assume your wife is in the 99, not the 1.
The reason you found a condom in her clothes was that they were planning to go off somewhere to have sex. Probably the woods walking the dogs ? Why she didn't use it ? Maybe because the other man brought one.
You have become a "boiled frog" in your marriage. Things have slowly got worse over time and you have made allowances and got used to to a new order - but you don't sound happy. What to do ?
I would say bugger it - and offer a divorce - but I understand you may want to get proof - otherwise it's an itch you can't scratch.
If you want proof - here's what I would do in your position. Buy a couple of spy cameras off ebay (with audio) - they are cheap (don't get them delivered to the house obviously). You can get them that are disguised as household objects - clocks, pens etc (Disclaimer - never bought one myself!).
Given that he visits the house when you are not there - place them where you think they will be - e.g. the kitchen - maybe even a bedroom. Then tell your wife you will be going out for the day (give her plenty of notice). Check the cameras - that should tell you whether or not the relationship has crossed the line.
Next step is up to you.