My advice is do not rely solely on the suggestions posted here, but instead, go to a lawyer who does bankruptcy, real estate, and foreclosure), who will be able to lay out all the options that exist given your unique circumstances, which include: bankruptcy, short sale, deed in lieu, etc... . You need to know the consequences of each route you may choose.
If a person cannot be located, but they have fled the country, then a process server can go through the due diligence and prove that the person left the state to avoid service of process. At that point, someone can serve by publication (newspaper summons) and that could establish jurisdiction, permitting a default and default judgment against the person who ran away out of state and was dodging service.
The legal answer is "no.". There is a myth about this: people believe that children get to decide where they want to live after a certain age. Not true. In reality, however, some kids control their parents or manipulate the situation to get what they want.
The answer to your question about the 1 year deadline relates to CR 60, which permits her to set aside (vacate) a DECREE based on 11 possible factors within 1 year. However, if she can prove fraud, misrepresentation, or a few other grounds to vacate, then she has longer than a year from when she discovers the fraud. If there was a lack of full disclosure, then yes, she could make this claim. What happens? If she wins, the court will not "undo" the divorce, but usually will allocate the...
The best move is to hire a lawyer in the County you last resided with your spouse. They will file all the mountain of forms you are required to do since they passed the law in 1991 that requires mandatory forms. Or, you can go to a stationery store or the courthouse and they sell packages on "how to get divorced: do it yourself." Do not hire a paralegal to represent you because it is illegal for them to practice law, but some actually do it. The initial cost is usually $240-250 for a filing...
You should file a written request with the court to change the name, but if you cannot locate him, ask the court to have a "special master" appointed to sign for the father in the father's spot on the dotted line.
The answer depends on what world you want to be in: (1) court, or (2) administrative. You are currently taking advantage of the free administrative process of having DCS try to get these amounts. They may or may not be successful. If it were me, I would advise you to go to the court world, i.e., file a order to show cause re: contempt to establish a judgment for percentage of day care expenses, and seek attorney's fees.