Thanks for your good question. Many people in similar situations have asked similar questions.
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My colleagues may have other views but here is my two cents.
I would say Yes, it is possible.
The Church would want to investigate your first marriage with your cheating wife, not just to get in the way of getting in a good standing with the Church, but because Jesus through His Church cannot bless bigamy and has to ensure your first marriage was not valid. Based on what you have told us, I don't think this will be a big problem.
They would probably want your first wife to cooperate with the Church in declaring your first marriage was null . . . meaning something was lacking between the two of you in the consent to marry. If your first wife does not want to cooperate, I think the pastor still has other options.
If your first marriage was declared null by the Church, because you are a Catholic, you would have to convalidate your current marriage in the Church, as the Church would not recognize any marriage of a Catholic that was not performed in the Church and yours was done in Las Vegas by a non-Denominational pastor.
The next best step for you to take is to talk to your local pastor and share with him what you have shared with us. If my colleagues have more to add, you will hear from them.
As a final note: To get in good standing with the Church also means knowing the faith. I would highly recommend picking up a copy of the Catechism of the Catholic Church. Also, find out what ministries your parish has so you can get involved with like-minded people in the parish.
I hope this helps,