My advice is to not take GH's advice here I actually don't think much will change in his sitch until he chooses to stop tolerating it as it is and he stops coddling his W. She feels no crisis w/him and there is no pressure on her to change.
Anyway, IMHO, complacency is not the answer here. What needs to change will not change and you will be right back where you have been with an R that isn't working for anyone. You need to ONLY accept an R that works for you on your own terms. Sure, your own terms should involve some compromise. But, this does not mean SO can waltz back in and pick up where he left off. THE OLD R IS OVER. Only a new R is possible, so why start off with one that you don't want to begin with?
RB is right that some very firm and clear boundaries about what will work in terms of him returning to the house are called for. And, you need to COMMUNICATE those boundaries directly.
It is crazy for him to just think he can move back home. You do not have to agree to live with him. I do think that your immediate reaction -- that you just run away -- is pretty much more of the same and a whole lot of regression from you.
My guess is that you are still VERY ANGRY about him living with OW and emailing her after your weekend. That anger is interferring with you working through this latest news. Instead, you are acting out by threatening to run away.
Get a grip. You aren't going anywhere with 3 kids without a job, childcare, reliable transportation, etc... As you noted yourself, it is more cost effective for SO to continue to live elsewhere. As I see it, until YOU are willing to live with HIM, his options are to stay in an apartment or get you a separate house with enough room for the kids and furnish it, etc...
This is not simply his choice. He is not simply entitled to come home. If he can afford a new truck and stuff to dress it up, he can afford to stay out of the house. If he is working less, he can babysit more so that you can generate income. There are many creative alternatives.
Now, I actually think that he wants to come home because he wants to reconcile. But, NEITHER of you are communicating in an open way. NEITHER of you are sharing your feelings in a way that can lead to productive conversations in which you actually work through anything.
I suggest that you really try to be honest with him about what is going on with you and your feelings.
I suggest that you focus on setting boundaries. These require telling him what you will do in certain conditions. Boundaries are not about telling him what to do. They are not rules for him, they are rules for you.
Why in the world would you consider, for instance, allowing someone to move in with you when you aren't in an R in which you can ask why he was emailing some woman he was involved with from your house?
Why in the world would you consider, for instance, allowing someone to sleep in your bed if you have no idea if they want an R with you?
If you don't express some of your hurt and anger over what has been going on, then I'd say the chances are slim for you to have any kind of successful R with SO. Right now your understandable hurt, pain, resentment and anger is toxic and polluting any kind of hopeful situation that is apparently arising.
Quit acting out. Take responsibility for your life. Communicate.