An appeal by your wife, even if successful, would not actually make you still married to her. It would merely re-open some of the terms of the divorce.
In order to appeal a court's order, a litigant has to point to some particular error of law that they believe the trial court made in the case. Merely not liking the outcome isn't enough. Strict deadlines have to be followed. You can't do anything to stop your ex-wife from trying to appeal, but she'd have to articulate a legal basis for it. Without knowing more about the case, we can't say whether she has one; but it's incredibly difficult to do it without an attorney. Under the circumstances you describe, her chances of success are pretty close to 0.
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You will get better answer from your own lawyer, who will actually give you legal advice rather then generalities.
It is possible to set aside defaults under Rules 59 and 60 if "excusable neglect" can be shown. The more involved a party is in a proceeding, and the more time has passed, the less likely this is. It is not a substitute for appearing. Terms or limitations may also be put on the set aside.
(Successful) appeal of a default judgment is unlikely; there would have to have been a whopper of an error by the judge in applying the law granting a default.
A motion to set aside default *could* be appealed, but it is rare to aside the trial court's judgment on this--he has considerable discretion.
It sounds like your main questions is whether you can remarry. If a Decree of Divorce has been entered by the court, you are divorced. Accordingly, you can remarry without having concerns about a possible appeal or setting aside the current decree.
She has 6 months to set aside the Decree for specific statutory reasons, or 30 days to file an appeal. Neither of these prevent your ability to remarry, though it might be a good idea to pause before you proceed too quickly. You thought this one was forever, and here you are on AVVO. To answer with any more specificity regarding her ability to set aside, you would need to have an attorney review the file and the court minutes.
The short answer is "yes" she can contest and appeal, but the timelines provided by the prior attorneys apply. What, exactly, she is or could contest depends on what the Decree states. If she wants to fight something, it will be about property/debt division and/or alimony/support. You will be returned to the status of a "married" person - so I agree with the statements on that. Most important, you should really keep the opinion and back-and-forth with your own lawyer who knows your actual case.