Well, color me weird, but I can give you no advice without more information. You have been together for more than a decade and I would think the issues that caused the split are therefore pretty serious, particularly given your comments about his cold shoulder, etc.
How you deal with it depends on the reason that he left the home and the issues that lie between you. I would suggest getting professional help for yourself, particularly as you are currently in a state of sitting and spinning, and if you go with a pastor, make sure that he is appropriately trained in counseling because many are not.
A book that would be helpful to you no matter how this plays out is Passionate Marriage by David Schnarch. It teaches about creating greater intimacy in marriage, figuring out what other life issues may be making their way into the bedroom and preventing a couple from really enjoying sex and growing together in that area, and it also speaks about differentiating as an individual so that you no longer "need" from your mate. When you reach this point, there is less finger pointing about who is doing household chores, if the person pays you enough attention, etc. Many of these are also relationship skills that go beyond the couple and will help deal with children as they grow older and figuring out the right things to do is more diffiult than with the younger child.
I do agree with the not pushing to an extent but depending on where his head is at, he can keep you in a state of limbo indefinitely and that is not a positive alternative to splitting up. Staying together is always the best option if it is possible but if things are going to end in divorce eventually, having gone through this myself and seen many other people, it is sort of like ripping a band-aid off the wound. Kids do adjust to their parents living in two homes and it is easier on them to go ahead and do that instead of sitting for months or years hoping mom and dad will fix things when they won't.