Check the terms of your child custody order to see if there were any rights that were granted to the other party on an equal basis as your rights (i.e. Access to school records, etc.) This will let you know what rights he may have in terms of parental rights as a non-custodial parent. It's hard to say if a judge would listen to a motion to change custody or pursuing visitations but it is also not unheard of. Talk with an attorney in your area to see what MD has to say about this and what protections you have in place already and what you can do further to protect yourself.
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As counsel indicated the custody decree is a good jumping off point. Whatever it provides controls until it is modified. That having been said, there are practical aspects to this. If his parental rights have not been terminated, and your question suggests that they have not, he has the right to ask for many things. Getting them is another matter entirely. I have been doing this for 24 years. In all that time, I have never heard of a judge ordering visitation in a prison. I suppose there is a first time for everything, but the court would have to find that the visits would be in the best interests of the child, which is always the standard. It would be a very difficult position to sell to the court.
Updates and photographs are a different matter. While I have never seen this before, it is something less of a stretch to envision a judge doing this under the right set of circumstances. It would depend largely on the particulars of your situation including the nature of the crime for which the father is incarcerated.
From the limited fact pattern, you have been granted the most important controls a parent can have for their child. Depending on the exact words of the custody order, there still may be avenues of pursuit for your child's father to pursue to gain some form of access to your child. That said, he would be limited to what a Judge is willing to grant him. A Judge would have to weigh the best interests of your child in making these decisions. If he is going to be away for "many" years, it may not be appropriate for him to have access to such a young child, not to mention she certain is not old enough or mature enough to understand. That is for the Judge to decide and for you to argue, either pro-se or with an attorney. I would highly recommend seeking counsel in this matter as a prison is no environment for a child. As stated earlier, I have never heard of a Judge ordering a very young child to prison visitation. Nor have I heard of such an order at any age. In the future, should he still be locked up, it will be up to her to chose what kind of relationship, if any, she may want to have with him.
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