This sounds complicated and fact sensitive. Generally, irrespective of what your will may say, the child's father would be the custodial parent if he has been legally acknowledged as the parent and his parental rights have not been terminated. You should both consult with attorneys or your choice (not necessarily the same one).
This answer does not constitute legal advice. This advice is based on general principles of law that may or may not relate to your specific situation. Facts and laws change and these possible changes will affect the advice provided here. Consult an attorney in your locale before you act on any of this advice. You should not rely on this advice alone and nothing in these communications creates an attorney client relationship.
You and the boy's father will have to first ascertain at what level he was sentenced under Megan's Law, and whether he has complied with all of the probationary requirements of his sentence. You should also gather together the documents that show him to be the father, such as a Court Order for child support, a Birth Certificate listing his name, and anything else that might support his position. In reading your question, there is a lingering question as to whether the boy's father might be visiting or otherwise involved with the child, which could violate the terms of his sentence. At this point, I am not aware of any Court decision that permits the Will of a mother to override the terms of a sentence that was imposed by the Court. For this reason alone, you should gather together the necessary documents and information so that you and the boy's father can determine how you will proceed. If all else fails, whether or not you include a statement in your Will concerning full right to the father, you should at some point in time make your sister aware of the Megan's Law conditions that apply to the father since she will be required to comply with whatever conditions are applicable to the boy's father.
A surviving parent has parental rights even if not so stated in the will of the parent who dies first. However, depending on the kind of improper child contact Megan's law offense, the parent's parental rights can be impaired. I would suggest getting the father's "record" so a lawyer can determine whether parental rights are impaired. Lawrence Friedman, Bridgewater, NJ. Certified as an Elder Law Attorney by the ABA approved National Elder Law Foundation, former Chair NJ State Bar Association Elder and Disabilities Law Section, Member Board of Consultors of NJSBA Real Property, Trusts & Estates Law Section, Vice Chair Special Needs Law Section of National Academy of Elder Law Attorneys, and Master of Laws (L.L.M.) in Taxation from N.Y.U. School of Law. Visit SpecialNeedsNJ.com for articles and Q&A on elder law, special needs, wills, trusts, estates, and tax and SpecialNeedsNJ.com/blog for timely updates. Information on both Avvo and SpecialNeedsNJ.com does not constitute legal advice, as it is general in nature and may not apply to your situation or be subject to important changes. No attorney client relationship exists unless set forth in written engagement terms.