I would take your daughter's feelings and opinions into account first and foremost and ask her biological father to give her the same respect. You said in the first post that she is ten years old and feels uncomfortable meeting her biological father. I would honor those feelings.
I would explain to her father that she's not ready to meet him and ask him to wait until she feels more comfortable.
I would try to explain to him that in the long run, that approach would probably have a much better chance of ending successfully in terms of any future relationship between the two of them.
He might feel ready to meet his daughter - but she's not ready to meet him.
And since she had nothing to do with creating this sad situation for him - he should understand that he needs to put her feelings and needs before his.
I'm thinking of myself at ten, and if someone told me I had to go meet someone I didn't know and spend a month away from my family where I felt safe and secure and stay with that person - I'd be terrified.
I adopted my daughter. She is and never has been interested in meeting her biological family, and not having been adopted, I can only respect her feelings and wishes - so I can't imagine forcing her to do that, especially at the very tender and emotionally vulnerable age of ten. There are all sorts of issues and feelings this sort of thing could bring up in her that if not handled sensitively could result in lifelong problems.
I'd listen to my daughter and ask her dad to have enough respect for her to do the same.
He owes her at least that much - it sounds like she doesn't owe him much of anything.