All of the above.
An international law lawyer has to find a way to work within different legal systems -- including doing research, sometimes reading or drafting contracts (but s/he has to be sure to meet the requirements of all countries involved).
Travel is definitely part of the job. . . and depending upon who you're representing (and in what type of an issue) trial could be a common part of the job, too.
An attorney who specializes in international adoption may well accompany his/her clients abroad to prepare papers for the courts there, and to represent clients . . . or may travel abroad to represent a client who wants to migrate to a new country. . . .
The field of international law is volatile and variable -- it encompasses so many aspects of law . . . they're just somewhere else.
If you feel that her or your safety is in danger, call the police. If he comes to your home and refuses to leave when asked, again, call the police. Trying to obtain a restraining order against this individual without the assistance of an attorney is not a good idea, as the procedures for doing so can be quite complicated. If you cannot afford to hire an attorney, try googling "legal aid" + your state or looking up your state bar association. Organizations do exist that specialize in providing legal services to those who otherwise cannot afford them, and some even specialize in assisting women seeking protection from stalkers/abusers.