Your wife needs to get some more tests done. This document talks about cases where just anti HBc is detected: http://www.wjgnet.com/1007-9327/12/1255.pdf
I quote:
The clinical significance of “anti-HBc alone” is greatly
unknown. Longitudinal studies to explore the long-term
clinical outcome are hardly practicable. We therefore
investigated all individuals found positive for “anti-HBc
alone” in our diagnostic laboratory over a period of 82 mo
in regard to their virological and clinical findings.
People with HBV do have kids, so that is not an issue right now. To start with, I recommend that you read
http://www.medhelp.org/health_pages/Hepatitis/HepB-Introduction--Welcome-Page/show/34?cid=153, and then keep us posted with all the lab results. I hope you are willing to read a lot; that is one way most of us have found to stay on top of the situation. This is especially important in your wife's case.