I’m so sorry in Op, he must think you came down in the last shower to believe that frankly bizarre nonsense excuse. It doesn’t sound like he can be bothered to even make up a reasonably believable excuse.
At the moment he is controlling the situation - cheating, telling huge porky pies to your face, carrying on like nothing has happened, all presumably before heading off for months to do the same thing again. You cannot move on from this as a couple if he is just barefaced lying and unless he accepts culpability and is honest and remorseful your marriage is over.
So you have three options as far as I can see: (1) accept the lies, challenge no further and decide to end the relationship now or at a time of your convenience, (2) accept he’s lying and stay together but be clear what the terms of this relationship are for you, i.e; cohabitants/room mates, no longer building a future together but just there for the children, no longer any loyalty from you. Or of course, option 3 which is sweep under the carpet and move on.
You need to take back control of this situation - some things to think about :
- Get counselling to talk this through with someone neutral and to try and work out what you want and what is within your control.
- Work out what would be best for you right now - it sounds like you’ve got a lot on your plate and perhaps don’t have capacity to deal with this, You could choose to focus on the most urgent things in your life right now (your son and Dad etc) and be clear with him you don’t believe him, you don’t know what the future of your relationship is but you’ll deal with it when you have bandwidth.
- You could tell him you don’t believe him, will never believe him, don’t trust him and can’t continue in a relationship with him as you know he is a cheat. Tell him you want to separate - see if he comes clean with the truth and decide based on what that truth is, what you want to happen.
- When is he away again and for how long? You could play the long game and just leave it for now but plan for your exit emotionally, financially etc. get your ducks in a row, keep your powder dry and use the time he’s away to make plans.
- Think very carefully before sleeping with him, of course!
- Do you have separate bedrooms so you can create distance even if he won’t leave the house?
- Stop cooking / cleaning etc for him -stop all wifely duties
- Stop being friendly, he’s got absolutely no shame or remorse. He is not your friend. Grey rock him.
I don’t think you’re ever going to get the truth out of him, you know what you heard, it crossed your boundaries and so in a way it doesn’t really matter what he says on the subject. Based on the reality that he cheated, what do you want to do? Stay with him and accept he’s a cheat, or leave?
He’s absolutely gas lighting you right now and it’ll drive you mad if you don’t take control.