His 2nd DUI within 3 years would be good grounds for a modification of custody and/or visitation, and for a request for monitored visitation. You would best retain an experienced Family Law Attorney to advise and represent you for that modification. Best not to let a habitual alcoholic to be with your child/children unmonitored.
Answer Applies to: California
Maybe, but it depends more on you than him. As long as you are clean and sober and not a threat to your daughter, a court would be arbitrary and capricious in awarding more than supervised custody with the father. However, he is the father and until you go to court and get a custody order, he has as much right to custody of your child as you do.
Answer Applies to: Idaho
You need to hire a Lawyer because the facts are on your side as well as the Law in Georgia because he has to do a Legitimation Petition to even be allowed any visitation and with two DUI convictions stopping overnight visitation should be highly possible.
Answer Applies to: Georgia
There is no way of knowing if there has ever been custody awarded under the circumstances that you describe because every case is so different. It is important that you go to court and get custody of your child. That way you can argue - and you have a good chance of winning - that the child should not be gone the weekend with someone with a clear alcohol problem. I would suggest that you stand your ground and I would do my best to get to the courthouse first. An attorney can help you with the procedural aspects and give you a better idea if they have all of the circumstances.
Answer Applies to: Alaska
You will need an attorney and his past will have a bearing on the results of a custody hearing. As the circumstances are described, I would doubt he would get have joint physical custody but he could be awarded joint legal custody.
Answer Applies to: Michigan
It sounds like the only reason the father is seeing the child is that you are providing the child. Since neither one of you has asked the court for a parenting plan, he has no legal right to see the child. My advice is that you file a Petition for Parenting Plan/Child Support (assuming that hasn;t been addressed either) and raise the issue of his alcohol abuse in the hearing, asking the court to order an evaluation. The history of his seeing the child will be part of what the court must take into consideration. Your allegation about tax fraud is worthless if he has neither been charged nor convicted. You are not judge and jury of his conduct. His alcohol issues, however, are significant as they pose a risk to the child. I assume when you say he has never been denied visitation, that you haven't ever not let him see the child when he's asked. That's nice, but has no legal significance since there is no order. It simply goes to the history of his involvement with the child.
Answer Applies to: Washington
Your question cannot be fully answered as there is no way an attorney would know about every case that has ever been filed. That being said, the tax evasion is not relevant. However, the DUIs are. The court is likely to restrict parenting time. In determining custody the court decides what is in the best interest of the child after looking at a number of factors involving both parents. Certainly, his drinking problem would be considered.
Answer Applies to: Indiana
Take his intent seriously, obtain counsel. It doesn't sound like you ever had a custody order or visitation order in place. In light of his drinking, no time like the present.
Answer Applies to: Oklahoma