Sorry you are here. It must be difficult on you since everything happened so quickly. Four months bomb to D. So you are still in shock I imagine.
I would suggest looking into counseling for you and your kids, especially your kids. It happened too quickly and your kids are at the age where things affect them big time. Look into local churches or community organizations for individual and group counseling. Check out a Divorce Care group (see divorcecare.com) in your area.
Let xH be hateful. It is okay. That is as much for him to deal with his guilt as anything. It is really not about you or the kids. He must demonize things to hide from himself. Let him move on and have little contact with him for now.
Hard to GAL when with the kids all the time? Try to leverage your kids in your GAL activities. When your kids enroll in things there are often other parents involved. Take advantage of that to make new friends – after all you have the kids in common and all your kids are in a similar age group. You may even meet other D people. Volunteer at school, PTA and church. Just some ideas. Save the romantic GAL for later.
The road is hard but you will look back and be thankful it did happen so quickly. You are closer than I in getting that new, wonderful life; I have been at this 15 months. Good luck.