J.B.
Neither. DO NOT start a new relationship. I know it feels good and is tempting, but, to be blunt, you are damaged goods right now and the only thing you'll attract is more trouble. Good, stable, loving, worthy guys don't dabble around with women who are still married to someone else. They just don't. A good man would say "oh, you're still married? Well best wishes to you. If you ever find yourself single and have had time and space to deal with ending your marriage and are ready to date again, perhaps if I'm not in a relationship at that time, things might work out. But you are not available right now."
You married a man-child. He was someone YOU picked. You have a bad picker. You need to end one mess, stand on your own two feet, parent your children, go to therapy and learn WHY you picked a loser and what you're going to do differently next time to make sure that if and when you're ready to date again, you don't pick ANOTHER jerk and put yourself and your kids through this again and again and again.
Time to tell your husband that it's too little, too late. Someone serious about fixing his marriage doesn't screw other people. He just doesn't. He's playing with you...reeling you in, messing around, seeing you get some space, getting jealous, reeling you back in, a messing around, and so on and so on.
Walk away from the BOTH. You need to clean up one mess before starting another. The statistics on post-divorce relationships aren't good...that vast majority fail, especially the ones that start before a marriage is actually over. The best post-divorce relationships are ones that aren't started until at least a year after the divorce is finalized and the marriage is really over.
Stop screwing around and diverting your attention away from what you need to do, which is go through the painful, messy work of really ending your marriage. Grieve your loss, pull yourself together, work on yourself, focus on your kids, THEN go out and date.