Husband Avoiding Divorce

My husband received a marriage-based conditional US Green Card and then promptly disappeared. I have hired a lawyer and am trying to get the marriage annulled on Green Card fraud grounds. However, he is intentionally being as difficult to find as possible.

Since he had refused to even tell me what state he was in for 4 months, my lawyer filed a petition for Notice by Publication. I was in communication with a mutual friend who apparently told my husband (I am no longer in communication with this person), and the next day my husband sent me the address of the hotel he is staying at in Florida but no room number. He said he will be there for at least a month. Since the court date for the Notice by Publication isn't for another 2 weeks, I'm worried the judge is going to say that I have to try to serve him. He has once again disappeared and refuses to respond to any text messages or phone calls. Do I now have to pay for him to be served at the hotel AND still go to the Notice by Publication hearing now? Since he is intentionally dragging this out, can I sue him for the cost of my lawyer?