very complicated marriage problem. Need honest input

Hello!

I want to warn you all that his is going to be a long thread. I would love any and all advice.

I almost dont even know where or how to start this. I figure from the beginning with background is the only way to go. My husband and I met when I was 15 and he was 16, we dated until 18/19 and got married.
When my husband turned 22 he started drinking. We would go to bars with our other ‘boring’ ‘couple friends’. By the time he turned 23 he was drinking alot. I would have a drink or two a night and he would have a half gallon of rum. By the time he turned 24 I was no longer drinking, and fights would start over his drinking (the waste of money, that he had a problem blah blah blah). Around his 25th birthday I had enough. I am extremely close with his grandparents (they raised him) and together we decided that I would ask him to move out. They arranged for him to come stay with him but, he could only be there WHILE SOBER. His grandparents and I knew we couldnt make him quit drinking, however we figured that he would probably hit rock bottom and change himself.
The day we through him of my house was November 29th 2012. During the next several months we would talk on the phone, text, or email a few times a week to a few times a month. Mostly when he was sober enough to remember I had existed. I felt like maybe I had made a mistake in not just leaving him and moving on. In January of 2013 I turned 23. He forgot my birthday completely and I celebrated with my family (my parents, siblings, friends, his grandparents and siblings.) They were all very supportive on what felt like the lowest point of my whole life.
In February of 2013 I got a phone call from the jail. My husband had been booked for meth charges. I had no idea he was doing hard drugs (or any soft drugs other than alcohol). I went to the jail and visited him the first weekend he was there. I informed him that I would not be bailing him out, accepting his phone calls, or writing to him. That I loved him but, he had chosen this path and must be an adult and accept his punishment.
He wrote me many letters about how he would change once he was let out, and when that day came in April I allowed him to come back to our home under some very strict conditions. In mid april, about two weeks being home everything was back to normal. I had my sweet loving partner back. He continued going to NA/AA meeting and I must say, to this day is still clean. However something else happend in mid April.
My husband sat me down and confessed to sleeping with 14 different girls from November to being arrested. I was upset to say the least. I told him that I would have to think about life and get back to him when I knew what I wanted to say.
On May first, I decided that, yes we had a really rough year. However, he was clean and sober and I could give him another chance (which let me interrupt, was a good idea. He hasnt cheated since, and we have the best relationship in the world.) It was a hard journey which actually involved moving to a different city about 70 miles away. I have truly forgiven him, I no longer think about what happened and trust him. I am willing to accept that he was very sick at the time. Please dont judge me to harshly for that.
Today (April 28th, 2014) I got a phone call on my cell. It was from one of the girls he had cheated with. She informed me that she had a baby and that my husband was the father. Apparently, the child needed diapers and she requested money. I tried to be as nice as I could and inquired if my husband knew of this child. She confirmed that she hadnt spoken to him since may of last year when she had contacted him for a booty call that he turned down and told her of me. (my husband had informed me of that..)
I spoke to my husband, we decided to send her $20 for diapers and requested that she give us a DNA test. After she agreed and he hung the phone up, I went into the bedroom. I told my husband that I need a while to think.
Truth is, I have never laid eyes on this woman but, I hate her. I hate that child. I know how horrible that is to say. I hope my husband isnt the father, and honestly I dont think I can be married to him if he is. My husband was tested before we had slept together, I know I dont have anything. However knowing that my husbands first child was not my first child will probably break me.
I dont want to be this child's step mother. I dont want any of OUR money going to this child. I dont want to share his time with THEM.

My question is, what should I do? If this is his child, what would you do? If you are a man, and you were my husband, what would you want me to do? Why?

Thank you in advance for any information,

Annie