Grounds for Divorce?

What is the name of your State? Iowa

I need some advice! I read that in the State of Iowa that cheating and physical abuse is not grounds for divorce...Is this true???
I have been married to my husband for almost 6 years now and have 4 children (1 was stillborn) by him. I have caught him cheating on me atleast 5 times since we have been married and once was with my aunt! He has physically abused me for years and was arrested twice for it before he stopped. I assume because he was afraid of being arrested again but he never stopped the cheating!
The last time I caught him was when I just got home from the hospital after having my youngest son who is now 10 mos old. I left in Feb. of this year and have been living with my parents ever since but I am ready for a divorce!
He doesn't want a divorce and insisits that he will NEVER cheat on me again but I have heard that story too many times before. I dont want to drag this through court and have to spend a lot of money that I dont have on attorney fees and court costs. Is there a cheaper and easier way to go through this? I am also wondering about the kids... will I automatically get full-custody of the kids since he has a history of domestic abuse?
If someone out there has any advice for me I could really use it!

Thanks!

Yes, Iowa is a no fault state. You ought to see a lawyer as soon as possible.

See http://www.divorcesource.com/info/divorcelaws/iowa.shtml
for more information.

Read carefully the sections on "Mediation" and "Custody". If he has a documented history of DV toward the children you *may* be able to get his visitation supervised. He also may be able to have you both partake in mandatory counseling if he feels the marriage can be saved. A "parenting class" is also necessary.

I would start out by filing for custody, CS and Alimony. Iowa is an "equitable distribution state" as far as asset/debt division goes.

Good luck.