That's going to depend what the laws are in your state in Brazil. Like I said, in the province my kids were born in and where we resided, informal (non-court ordered) parenting agreements are recognized and encouraged, so we have an informal, written parenting plan agreement. It is written in a fashion such that if something did happen and we were spending too much time disagreeing about the kids, that we could file it with the Provincial courts to formalize it. If we came from a different province, that was unlikely to be the case. Because it was the case, having the lawyer notarized letter from the children's father very directly acknowledging we were immigrating on a permanent basis in conjunction with that parenting plan agreement, it was accepted. Canada also isn't a high fraud country, so that likely played into the acceptance decision.
So, check your local laws on parenting plans. Also check the local laws on taking your child internationally. If you are required to have a parenting agreement, find out if you and your child's father can write it, following a template and submit it to the courts yourselves. That route is typically pretty inexpensive because no lawyer is involved. If your state doesn't require it, you'll still have to sit down and write an agreement between the 2 of you to present with a letter of consent for US immigration. Make sure you understand the legal wording in both Brazil and New Mexico. For us, there were slight differences between our home province and Texas, so I included verbiage that covered both places. For example, you can have joint custody, but defining yourself as the primary, custodial guardian who has sole decision making authority for things like healthcare in the US are important. Back home, "guardianship" is defined, but "custodial" isn't a legal term used. In Texas, courts use "custodial parent and not "guardian". We make sure to include the equivalent legal defined name for the terms from both countries. You should also define your fiance's role as a step parent in the agreement.
The Hague Convention exists for a reason - too many parental kidnappings, so informed, parental consent is paramount in any immigration case.
Its hard because those individuals who can't get along and coparent effectively ruin it for the rest of us who can peacefully do so. I understand how important permission is when it involves taking a child internationally, but it's still pretty astounding how many people really aren't looking in the best interests of their kids! I'm happy to hear you are another co parent who stands beside me in making peaceful decisions in the best interest of our children.