According to Rhode Island statutes:
"§ 15-7-4 Petition to adopt – Court having jurisdiction. – (a) Any person residing in Rhode Island may petition the family court for leave to adopt as his or her child any person younger than him or herself and under eighteen (18) years of age, and, if desired, for a change of the child's name, but the prayer of the petition by a person having a husband or wife shall not be granted unless the husband or wife joins in the petition; provided, that upon good cause shown and a showing that the granting of the petition for adoption would be in the best interests of the minor child, the prayer of the petition may be granted although the spouse of the petitioner is not a party to the petition.>
"§ 15-7-7 Termination of Parental Rights...4) The parent [in this case, your ex] has abandoned or deserted the child. A lack of communication or contact with the child for at least a six (6) month period shall constitute prima facie evidence of abandonment or desertion. In the event that parents of an infant have had no contact or communication with the infant for a period of six (6) months the department shall file a petition pursuant to this section and the family court shall conduct expedited hearings on the petition.
(b) In the event that the petition is filed pursuant to subdivisions (a)(1), (a)(2)(i), (a)(2)(iii), or (a)(2)(vii) of this section, the court shall find as a fact that, prior to the granting of the petition, such parental conduct or conditions must have occurred or existed notwithstanding the reasonable efforts which shall be made by the agency prior to the filing of the petition to encourage and strengthen the parental relationship so that the child can safely return to the family. In the event that a petition is filed pursuant to subdivisions (a)(2)(ii), (a)(2)(iv), (a)(2)(v), (a)(2)(vi) or (a)(4) of this section, the department has no obligation to engage in reasonable efforts to preserve and reunify a family."
I must say it's sad that as young as your children are, they're already asking for adoption...that shows a real lack of a loving relationship with their father. I hope for their sake, as well as their siblings' sake, they still see his other two children, even though they don't see him? I know it may be difficult for you to facilitate that relationship, but it would be better for all the children if yours can still maintain a relationship with their other brothers/sisters. I would be happy to talk more with you about that in private, as I do have experience with that aspect of this whole situation.
Normally adoptions and things of this nature get handled through probate court (at least in CT, where I live); I suggest you consult a lawyer ASAP. He/she can give you the proper guidance that you need to move forward with the adoption and name change.
You can contact your state's Office of the Child Advocate here: http://www.child-advocate.ri.gov/index.php
They should be able to give you a direct link to more resources available for help with your situation.
One more caution: Don't be surprised if this jolts your ex back to reality. He may not realize what he's got 'til it's gone, so to speak; he may try to fight you at every turn to "keep" his children, even if he hasn't been acting like their dad for years.
Good luck with all this and congratulations on your upcoming nuptuals! Send me a message if you'd like to talk privately also; as a stepmom myself I have some insight.