Lucy.
It seems to me that that your H really doesn't "get" this, I'm afraid.
During that bank holiday weekend, he should have entered into family time with gusto, because this is what he stood to lose, wasn't it? A man in his position should have been pinching himself for his luck, not behaving like a spoilt teenage boy being dragged around clothes shops.
He is also being guarded with his phone and within weeks of discovery, is attending business trips away from home overnight. He is also failing to answer his phone, when he knows that it is the most understandable thing in the world that you want to contact him.
What you and Bella also say about how lazy, unhelpful and disengaged your Hs have been in the past is very illuminating too.
Affairs are an extreme manifestation of selfish behaviour. Basically, these men think the world revolves around them and they won't do anything they don't want to do. If they have to do something, they will do it badly, or with poor grace.
The advice you have had about creating a new marriage must involve all behaviours. This is your chance to list all of the things that must change in the future. You will never get the opportunity again to make these conditions.
The other thing I wanted to say to you is don't stay with him because you think it will be a better option to being on your own. In the short term, some things are going to be practically more difficult, but honestly, after a betrayal like this, you should be staying for one reason only; because you love him. Even then, you will need to be convinced that he has the capacity to change and will never do this to you again.
Based on what you've said, I really don't think he is in the right place and I'd have no confidence that this couldn't happen again.
Have a really good think about what you want from your marriage and try to be brutally honest about whether he has ever really delivered your expectations.
When infidelity happens, it is understandable and appropriate that one's tolerance for other faults (laziness etc.) vanishes. You cannot and should not "bargain" those faults away any longer, but see the infidelity as typical of a person with those selfish traits. If the selfish behaviour isn't eradicated completely, then the potential for further infidelity will always be there.