For starters in this case, extradition shouldn't really work like that. There is no reason a suspect cannot be jailed somewhere close to their home (ie near their family), with police from the distant jurisdiction doing the traveling to question her etc. Doubly so if she's able to post bail. It's the police's day job versus the suspect's life, right?
But as to basic situation, the fundamental problem is that there is no expectation of justice at the end of this.
There isn't really a way around the police (and judges who approve warrants etc) just doing their thing and you having to comply. But if it turns out they were wrong, then they should always be on the hook for all the damage they've caused - the same as every other member of society. In this case, every day the victim was held in jail, her costs of having to hire attorneys and private investigators to represent her, plus simply the distress of having this hanging over her head while being threatened with years in prison.
The article implies this has already been going on for six months. While this isn't a long time as far as the legal system goes (remember, day job), it's an eternity for someone on the receiving end of it. That should be well north of a million dollars for disrupting someone's life that long (especially over a frivolity!) - putting aside any abuse suffered in jail, direct reimbursement for expenses, etc. I want to say it should be more, but $5500/day seems in the correct neighborhood (a daily rate should be much higher for days you're actually in jail, but lower on days you're "free" but are still under attack).
This would create a strong disincentive for incompetent (or in this case, constructively malicious) action by police/prosecutors, as well as demonstrating to all citizens that the justice system actually tries to get correct answers rather than harming innocent people and then merely wiping their hands of it.