Don't worry about a new status quo. She is doing something criminal (custodial interference) and no judge will reward that behavior! If you don't know the address and have no way to contact the mother or children, that is kidnapping, and you should contact the center. Same as if on a visit a parent never came back with kids. They should put out a missing children poster with the pictures of mother also and date that they disappeared, I have seen posters many times where non-custodial parent took off with a child. If that is not kidnapping, I don't know what is. Somebody has to get the ball rolling here.
If you know her address, I don't see why you can't call the police in her area and see if they will cooperate with you to get your children. It will save you the trip if they won't and tell you that over the phone, but it would be the fastest (although perhaps traumatic, but I don't think you can do anything about that). Plus they might point you in the right direction. As far as residency, they aren't establishing residency because they are being unlawfully detained "against their will" (your will really, but you are the custodian so you determine their will).
But...different states have different procedures for enforcement of child custody agreements from across state lines. It may be worth it to look up her states procedures. Your state seems to use contempt hearings, but the other state may use a writ of habeas corpus, which I have heard is faster...I think. There is a new interstate child custody law that makes enforcement of a custody order across state lines much clearer (and it uses a writ), but it has only been adopted in three states. If she lives in one of those (MA, VT or NH 2010) things might be faster...in any case, some states have better procedures than others. Under the current law, enforcement is vague, thus why you are getting a lot of different advice. Depending on the local authorities, state procedures (maybe even the particular officer that you get on the phone) ect, will determine which of the advice would work the best in your situation. I would take the comment you heard about her DA with a grain of salt, because it might just depend on his mood that day, and he might just help you out too. Where are you and where are they?