Can My wife file abandonment charges on me ? She is the one that moved out, She refuses to let me see my kids, Never was a court order to pay any child support, No separation filed, and I'm canceling the divorce...

First, ANY question on law needs to include your general locale as laws vary by area.

Second, generally child abandonment is a criminal charge that occurs when a child is left without any adult supervision. So that would not seem to be the case.

Except in a very few states, she cannot file abandonment charges since there is no such thing. She may try to use abandonment as grounds for something else like getting a divorce, getting sole custody etc. But she can't just file for abandonment.

But if you want to see your kids, and I assume you do, you need to get into family court,

Also you can not "cancel a divorce" you can fight it, make it take a few years, but if she wants a divorce she can get one.

You need to be in family court filing for at least visits with the kids

I absolutely want to see them, She will not let me saying that I stopped giving her money every month. My attorney said that sense I was the one that filed the divorce I can drop the divorce because I stayed with her for a couple of days at her condo trying to work things out. ( the divorce was not finalized ) . She does make more money than me and if I get any communication saying that my kids need anything I will get it right away. The reason I don't want to give her money every month is because she took a U-Haul to the house and took everything, by that I mean you walked inside and it looks like your buying a new house ( EMPTY ) I live in GA.

First, when you have a follow-up question or info, please use the Answer options, not Comments.

So you live in GA, that changes my answer. In GA they call failure to support child abandonment. So if you don't provide support for your children you can be charged and arrested for child abandonment. Your lawyer should have explained this to you.

Visitation, cleaning out your marital possessions have NO bearing on support.

So you need to go back to court IMMEDIATELY and file for custody, visitation and support, before she swears out a warrant against you. You need to get the court to rule on how much support you need to pay. And to rule on when you can see your children.

As to her cleaning out the house, you need to try and catalog what was there so you can demand an equitable split of your possessions. And I would reinstate the divorce petition.

Scott, first off I want to say thank you for your help. Sense I filed the divorce I was getting my kids one day a week and every other weekend and I was paying her 500 a month.
I have not paid her the last 3 months because I haven't had the money. As far as the stuff in the house I really don't care about it, all I have asked for is my kids. I will send her something based on what you have told me, but My lawyer agrees that I have more rights to my kids NOT being divorced than I would if I was divorced.

I'm not sure I agree with your lawyer. Right now you have equal rights to the children. If you wanted to take them to live with you, there is nothing she can do about it until a court rules otherwise. But, by the same token she controls access only because there is no court order to the contrary. That's why I think you need to go to court to establish custody and visitation. Get a court to say you get to see the kids every other weekend and x amount of time during the week and she will be in contempt of court if she refuses.