What will happen is that the DVRO will remain temporary and it will not become permanent until after you have been served, a hearing is conducted and your ex proves (if he proves) that the permanent is necessary and lawfully required. The Temporary DVRO will remain temporary for so long as your ex continues to appear in Court (the Judge will continue to grant extensions of the T-DVRO), and if at any time your ex fails to appear then the T-DVRO will be quashed and that will be that.
Regardless, so long as it is a civil DVRO then it is not a criminal matter, there is no warrant attached, you are not a fugitive, your name will not be entered into a criminal justice data base, and so no, you will not be taken into custody (not for this anyhow) when you return to the States. You may be served (although I highly doubt that the Sheriff will be waiting around the terminal for you to return), but in the off chance that you are served then all that will happen is that you will be handed papers which will notice you of a future hearing in civil court (and you will be afforded sufficient time to retain counsel and prepare a meaningful and effective defense).
As to the rest of your question: “Can I sue _______”, this is not a criminal defense question; It is a civil law question.
Last I checked this was still America, and in America you can sue pretty much anyone for pretty much anything. Whether or not a) you can find a lawyer to sign her / his name to the paperwork, b) your lawsuit survives a motion for summary judgment / to dismiss, c) you get a favorable judgment, d) your defendant is collectable or e) you ever see a dime is both beyond my ability to predict and is anyone’s guess.
If you want to increase your odds at getting a competent answer then you should repost this question and list “lawsuits and disputes” and not “criminal defense” as a practice area. In fact, I will do this for you….
I hope that I have been helpful in properly re-directing your questions.
