As TS said above...both of your (you and TS) current problems are largely a result of yourselves. You talk about detaching, you ask about detaching, you have garnered answers to detaching, yet you are not succeeding in it.
You talk about how hard it is to gal and you come up with reasons to explain why you aren't. I would like to see you change your thoughts from why you can't gal to why you should be. Make gal'ing a goal for yourself.It can be with the kids, with co-workers, or just yourself. For the next week make it a goal to walk (with the kids) or run at least 1 hour everyday. No excuses....if you don't have a stroller then carry the kids...No running sneakers...then get some. No more excuses and more doing.
As for the separate households. First, I definitely agree with making your bedroom a one room apartment. Stay in there and it is your space (the shed to). I also think you should consult a lawyer before anybody moves out. Rules are different in other countries and you need to be aware of the kids (as a side note...You also need to think about CS in the future. The truth is 2 of the kids aren't really yours and you need to think on that).
I also think that you need to stand firm in that you are not leaving your family. You did it in the past in 2 days, you did it by cheating, and now it is coming up again. Now that is a 180 for you big time.
Finally....Work on Mach's questions....burn them into your mind and soul.