There is no real quick way to speed up extradition. You will have to let the process play out. This is done sometimes to sweat the inmate into a plea agreement. Finding a good attorney is not the easiest thing to do or the cheapest. You will have to talk with your daughter and get a feel for her case.
No one really "knows a good criminal attorney" unless they have been through a criminal TRIAL and been found not-guilty. THAT lawyer is a home run.
Here is what 98% of the attorneys will tell you. "You have a great case, we are going to kick their butt. I used to work in the prosecutor's office or for the FBI, I know this and that." They will sell you on how great they are and do their very best to convince you to give them a sizable retainer. Actually, the retainer is a made up number, it is literally "how much you have". They will take whatever amount you say you have, the whole thing. After the check clears, it'll be tough to get a straight answer about how the case is progressing. All this time, your daughter is rotting in the county jail. She is getting antsy. Then after a couple, three months your attorney will tell you, "I've reviewed this case, I've spent hours and hours researching this... I would recommend that she pleads guilty. The risk of going to trial is that if she loses, she will do 20 years, I can get her out in three to five". He convinces you to take the plea, she goes to prison and he will keep every penny you gave him, without lifting a finger except to pat his wallet. There is a lot of truth to what the lawyer is telling you, though... but you needn't spend your last dollar to hear it from them. If your daughter is truthful with you, you will have to weigh the cost of a trial against the potential sentence if she loses. Of course everyone is innocent in the beginning. But most defendants have some degree of guilt and it is up to you both to decide how much of a gamble you are willing to take, both with money and with the ultimate outcome if found guilty at trial. The sentences for offenders pleading guilty and taking responsibility for their crime is a fraction of what it would be if you lose at trial.
Save your money unless you are 100% sure you have a chance. Any public defender can plea bargain a sentence - it doesn't take much savvy to lay down and give the other side the victory. If you are going to trial, then the Martindale-Hubbard directory has the names of the top legal minds in the country. You ask them only two questions, "How many cases have you actually taken to trial? and How many not-guilty verdicts have you won?" All the rest of their story has little impact on whether you should hire them. The price for the best starts at $100,000 and goes up.