You do not require your wife's signature to finalize a divorce; the only signature you need on the final divorce document is the judge's. Compared to yesteryear, divorces are easy to come by in modern America, with all 50 states offering no-fault divorce that does not require spousal agreement or proof of bad conduct.
It is always easier when both spouses wish to divorce, but life doesn't always work that way. Sometimes only one partner is ready to call it quits, but one is all it takes to get a divorce. One spouse files a divorce petition and serves it on the other -- and the divorce is in process. Whether the other spouse files a response or not, the case moves toward divorce. The divorce is entered when the judge signs the final judgment.
You may move ahead faster with the divorce, however, if you can get your spouse's signature -- but on a marital settlement agreement, not the final divorce papers. Resolving your financial and child custody issues amicably puts your case in the fast-lane to a finalized divorce. An experienced mediator may help your spouse see the wisdom of settling issues amicably and help the two of you find middle ground. After your spouse signs the agreement, you will still need to have the judge sign your paperwork and finalize the divorce.