I thought that getting married for the second time would be better than the first marriage...
Boy, was I wrong!! Fraud (Fam. Code, § 2210(d)).

My second wife and I are currently going through an annulment/divorce. Right after her green card restrictions were lifted, my wife immediately abandoned our marriage. She lied and told me she is just visiting her mother for a week, but never returned. A week later, she told me over the phone that I am being investigated for molesting her adopted daughter, (her mother is alive and well in the Philippines). These allegations are false.
For months, (without my knowledge), my wife took her niece to the doctor while I was working swing shift. My mother and eldest daughter lived with me during our entire 3 year marriage. My wife would come home after 5 o'clock, pick up her niece, and she would come home around 8:00 or 9:00 p.m. at night. She lied and told my mom and my eldest daughter that she was just at the store shopping; however, I did not find out the truth until a week after she abandoned our marriage and told me this over the phone. (May I remind you that she did not confront me nor told anyone in my house about any accusations.) The social worker decided to drop the case because when the police arrived to question her niece, the niece ran away from the police and refused to cooperate. Social worker kept trying to conduct an interview with niece, but was unsuccessful.

In February 2009, when she found out I was filing for annulment/marriage fraud, she kept leaving me voicemails threatening to use molestation accusations to intimidate me if I try to annul the marriage.

FYI: Despite all this anxiety and stress, from the time she left - July 2008 to February 2009 - I asked her many times to come back and work things out with me; however, she refused. We are expected to return to court and this has been a long, exhausting, and stressful process just trying to annul this marriage. After all this, I realized how this woman manipulated and pressured me into marrying her during a vulnerable time (the time where my 25 year marriage with my first wife ended because she cheated on me) for a free ride and US Citizenship.

Please provide whether I have a strong annulment case that will or should be granted?

I am so sorry that this has happened to you. If I were you I would call ICE and see what you can do. Im sure that you are her sponsor and you are responsible for her financially and legally for 5 years from the time she arrived here in the states. You need to get that revoked asap! You don't want her running up stuff and getting you in trouble for it. I have a friend that called ICE after he had been here for 2 yrs. (same situation) and they deported him. Hope this helps and good luck. They seem to like to prey on innocent people and it sucks.

Nobody can answer your Immigration question because that will be determined by court depending on your case In the Philippines, most common used term for separation is psychological incapacity (irreconcilable differences for divorce). If you will be convicted for molestation and be imprisoned for say 20 years, annulment will be highly granted.

You are currently living in the US and obtaining a divorce is easier on your part. Annulment is very difficult to obtain in the Philippines and since she returned on motherland, it may take several years for her to get married in the Philippines. You can both obtain a divorce in the US even if you married abroad.
My opinion is you are not tricked for green card. Why she came back in the Philippines in the first place if she's just after green card?

Things just didn't worked for you and your wife after a tedious 1.5 years process in the immigration. With molestation involved, your communication just didn't work hard enough. She's torn to believe you or believe that you molested someone. If you get convicted and be imprisoned for 20 yrs, annulment will be highly successful.

Only wicked but we can't tell who who wants to go through hell in the immigration if she didn't love you at least. She spent time with you, had sex, make your meal, iron and clean your clothes and in return you provide for her so it's just even.

The bottom line is not the marriage fraud. Things just didn't work (called communication) after being really together. I know you are very frustrated and you may call this thing ICE that tenstepper is saying but think what I said. Men always think that they're used specially if there's "money" involved when things end wherein fact, the woman is not just happy. "Money" is not everything.