Your wife doesn't need to "sign the papers" if you file for a divorce. When a petition for divorce is filed, the papers can be served upon your spouse by personal service, certified mail service, or other authorized method of process service.
If you mean that she wouldn't sign papers resolving the case, then that too is addressed by the court entering orders at a final hearing.
The rest of your "question" is more complex. It certainly indicates that you and she probably should divorce. And there are many ways to get that accomplished. How much it will cost to get that done depends on the lawyer you hire, the complexity of your case (including what kind and how much property or debt you and your wife have accumulated, what other disagreements you and she have over other things, and other issues). But the factor that most affects how much a divorce costs is how much emotion there is over the divorce itself, and how agreeable both parties are in getting the divorce finished without a problem. That's where your question indicates problems.
There are some cases that take only minimal time and effort to finalize. But when one or both parties are angry or unreasonable, a divorce can cost many thousands of dollars (or tens of thousands). Call around, look up area attorneys, and find out about those attorneys' rates, experience, and case handling philosophy. Don't think that merely because one attorney has a lower rate or charges a lower retainer, that your final bill will be lower -- it likely won't be. Search for someone who can get your case finished with a minimum of drama, rather than one who promises to "fight fire with fire." You'll be ahead in the end.
This response does not constitute legal advice and does not create an attorney-client relationship. I am licensed to practice only in Kansas. Seek legal advice from an attorney in your state or the state in which your legal claim exists.
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