This is the kind of question you ask an attorney in North Carolina. Quite honestly, Washington does not deal with these matters in divorces and most states generally ignore any potential criminal liability for these issues as well.
If NC has "grounds" as a necessity for a divorce and you have a pending case there is not a large likelihood that you have to worry about a Statute of Limitations since the action is already pending. A statute of limitation deals with the initiation of the action, not concluding it.
Finally, I am somewhat surprised that you need her signature on final papers to divorce. That would seem to imply that she could prevent the finalization forever. Why not set the case for trial and let the court make a ruling?
You really ought to hire a lawyer, given what you have indicated.
Generally speaking, if you can prove that she had an affair she is barred from receiving alimony.
You don't need her to sign an agreement prior to getting divorced. As long as you have a claim pending for equitable distribution, it may be time to proceed with the divorce. Unless she has filed a claim for alimony, the divorce being finalized will cut off her right to pursue that claim. Talk to a local family law attorney about the financial situation and the extent of the marital property that needs to be distributed and
determine if it is in your best interests to proceed with the divorce now.
To file for divorce in NC, you do not need her permission or for her to sign some agreement. Just 1 year of separation and 6 months residency of either party. It is true that you need to serve the lawsuit papers on her, and some methods will require a signature. But not all.
From your limited facts, I assume you all are trying to negotiate a separation agreement and that is what she will not sign. We don't have enough information here to know what all the proposed terms are of any such separation agreement are, the details of the marital estate (assets, debts, incomes, etc.), and what would be a fair proposal therein. But some parties cannot agree, but that doesn't mean they have to remain married forever.
As for your specific question about alimony, unfortunately, alimony is very discretionary in NC. It's not a set formula or has a chart (like with child support). Income is certainly a major factor, but there are actually up to 15 factors the court may look at depending on the facts and parties. Here is the statute:
Marital misconduct is one of those factors. But "an affair" is also not enough information. Do you have proof? Was there actual sex? Or just dating, texting, calls, and other suspicious behavior? Only "illicit sexual behavior", as defined in the statutes, will generally bar someone from receiving alimony. Not merely an affair, and especially if no sex in said affair. Here is the definition:
(see subsection 3(a))
The responses contained herein do not form an attorney-client relationship, nor are they intended to be anything other than the educated opinions of the author. The responses may or may not apply to you and should not be relied upon as ACTUAL legal advice. Rather, what is being provided here is legal information that would be best followed through on with a consult with an attorney after learning more about your specific facts, needs, legal issues, and goals.
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