My fiancé wants to adopt my children and my children want him too. They have nothing to do with their birth father. We are wondering what the process is and about how much it will cost? What happens if he does not approve?

What will it cost, a fortune if the bio-dad has not signed off his rights. What has the bio said/done to indicate he would allow the adoption?

There is no way to tell the costs as that is totally dependent on the situation your in and on where you live along with the courts your going to use.

If the bio dad is willing to sign over his rights and permission, depending on the attorney 3 to 6 K around here.
If there are multiple fathers or reasons for additional hearings, more.
Each case is so difference best to talk to an attorney, maybe a couple and get estimates