You need a family law opinion here. Then with the knowledge they provide you know what your rights are and are not. Sadly this is another case where legal in one state is not legal in another. I’m not saying any state has the complete answer on custody laws. Parental alienation is what this is touching on and definitely is not a subject to be aired in front of or within hearing distance of any children. But with that being said parental alienation is a crime in some states and more needs to be done to prevent it from happening. Whether any of us had great childhoods or not, don’t pass it down to another generation to learn, let’s let kids be kids once again and take joy in that fact.

I agree, you need a lawyer for advice. Especially since, in the eyes of the law...you're not the parent any longer.

You might also look into counseling to get a better idea of how to deal with this.

Beyond that, be really careful who you introduce to your former in-laws. Make sure that they're squeaky clean and won't rise to any bait if they are taunted. And make sure that you know them really well...as in 2-3 years, not just months.

Honestly, if you're afraid that the meeting will drive your fiance away...then maybe he's either not the man for you, or should stay out of this?

As you only see her once a month, maybe just go ahead and agree to keep her away from your fiance/husband? While her adoptive parents have complete control until she's 18 on paper...in reality, once a kid gets to be about 15. Courts start listening to them more than the adults. So it might not be as long of a wait as you think it might be. I know that 5-10-15 years seems long now, but time flies.

As a legal stranger to several current "mixed custody" arrangements, and the hidden agenda of some of the "ex" themselves and their relatives, I would say this. Clear your feelings separately first. Write them out completely and in private. Put it aside.

Do not be in a hurry to share a discussion with the adoptive grandparents. Take the time to consider how your relationship connection actually happens. How involved with the birth father's opinion are they (based upon previous discussions). Consider the option that they are already aware of the current fiance and they want to be able to "see" for themselves, after they've already heard the son's version, which is going to be slanted to make him self look better than the "new guy".
Do Not Make any agreements at this time.
Take time to consider how often you see your daughter, what arrangements you already have in place, what works best for the relationship with the daughter.
The fact that the adoptive grandparents already have a negative opinion leads me to believe that this next option might give a positive result no matter what happens.
Your fiance is in a relationship day-to-day with you.
Any adjustments should be at that level.
Do not add the adoptive grandparents to the mix, and if you meet them out in public, then speak kindly, gently, short, sweet, and simple, and step away. Do not linger for discussion.
This will force them to consider their opinions based upon their personal interaction in public, no notice, no discussion, and provide a better way to gauge their true feelings.
Child#1 is living with her birth mother. Her birth father is in military, traveling to different bases, gone frequently, and rarely sees her. They stay in touch through telephone. The parents never married. Child#2 lives with his birth mother, who recently remarried. He shares the same father as child #1. The father's mother and step-dad live in the same area, and child#2 recently moved back, so this Christmas holiday means that if his dad is in town, dad will be visiting with him. Turns out that the grandmother makes the arrangement and is in limbo until son is able to determine his time in town. It really depends on how the arrangement you currently have is stable for both you and your daughter. This arrangement works for the parents, places the flexibility for the grandparent and as difficult as it is to keep the feelings positive, they make it work. Of course, they vent in private away from little ears and little mouths that carry words elsewhere.
The children are growing up understanding that people who do not like each other can still be civil, can still be polite, and be positive in their conversation.
I hope this helps you to work through your feelings. It's so important to figure out your "break point" and get it in balance so you can be positive.

No sure I have this correct but it sounds like you have no legal rights to the child. That means you don't have any legal standing and you're wasting your time and money getting a lawyer. They will tell you the same thing. I am a retired lawyer.

Not to be the negative one based on what you typed you don't have to answer just think. Why do you not have custody of your child? They have legal custody that gives them all the power sadly