Hello. Based on the facts as you stated them to be, I urge you to have private attorney counsel in this matter. Adoption is a complex process. There are many more questions to be asked and answered prior to providing you with appropriate legal advice for your needs and goals. Some attorneys, myself included, will confer for free, at no charge. Then, if legal work is performed, some attorneys, myself included, will provide a reduced fee for need. All the best to you and your family.
Tricia Dwyer, Esq., Minneapolis, MN, Family Law, Child Custody & Child Support Law, Rule 14 Qualified Neutral, Minnesota Supreme Court Roster Mediator, Tricia Dwyer, Esq. & Associates PLLC, Phone: 612.296-9666 EVERY DAY OF THE YEAR until 8 p.m. daily. See www.dwyerlawfirm.net
The short answer is yes, a private party can file an action to terminate parental rights. However, I agree with my colleagues that have already answered that you have some complicating facts. If you have resources for an attorney, it is a good idea to find one you are comfortable with to address the issues each in turn.
You can file a private termination petition. However, this is one of the most complicated legal procedures under Minnesota law. You have other options you should pursue first if you are thinking about adoption. I suggest in any event you retain counsel if you are serious about this adoption.