If my wife took money from work buther employer claims it to be more than she took, do we fight the amount in court or would be better to pay back?

If paid back, it would be easy for both you and the employer to characterize the occurence as a mistake, not criminal action. Note however that repaying the amount does NOT mean that it cannot be reported to the police: taken money that does not belong to you (e.g. embezzling from an employer) is a crime, and a crime does not become "uncriminal" because the perpetrator returned what he or she took. As stated, all the parties could decide to treat matters as if it had been a mistake, but you need to understand that it is possible the money could be returned and the theft reported to the authorities anyway. That, clearly there is less motive to do so when one has received back what was taken; and repaying the money would count strongly for lienance if the police were involved.

Note that if the money is not repaid, the employer can also sue for its return. It would have to prove the amount taken to recover it. If the money is returned, in an amount satisfactory to both sides, then if you make sure to get a a written release from liabilty (i.e. that in exchange for repaying the money, the employer drops any civil claims), yoiu can ensure you aren't later sued.

This is a complex decision, and there is no single right answer as to what to do. Given what is at stake--not "just" $8,000, but potentially your wife's freedom (you can go to jail for more than a year for stealing $3k or $8k), you should consult in detail, in person, and in confidence with an attorney about what to do in this situation.