There are many details that we would need to know about before advising you on the probability of modifying the current order. I recommend you sit down with a lawyer and discuss the case fully.
You will need to schedule an appointment with an experienced family law attorney in your area who can give you more specific advice. I would suggest that you gather as much information as possible to support your position that the children should live with you and take this information to your appointment, including the docket sheets confirming the other parent's criminal record.
My response is based solely on the limited information contained in the question. It is not meant to substitute your attorney's advice.
If your children's father has been non-compliant with the custody order your immediate remedy would be to file for contempt, but it sounds like you may feel that it is in the best interest of the boys to be with you and to have them in your primary physical custody rather than just try to get the father found in "contempt." If you petition to modify custody you will have to demonstrate that it is in the children's best interest to be in your primary care. There are a host of factors that the Court will employ and also there should be consideration of any criminal conviction and criminal charge. Like the other attorneys advised, you should review all the aspects of your particular relationship with the father and how he cares for the boys as well as his conduct under the current custody order with an attorney to evaluate your chances of gaining primary physical custody.