Now that we've gotten
to know each other, our representatives can get together
to work out a schedule for our courtship. I have a few travel commitments
that have to be worked around. Unexpected problem occured and she needs to travel
to solve it?
No, no. "Work around" can be used literally:
(Flora wants to vacuum the living room) "I'm sorry, Flora, but I have these piles of paper in a certain order and I can't move them now. You'll just have to work around me."
or, as in this case, to indicate that appointments will have to be moved around and perhaps obligations shifted.

In other words, they will have to take her travel commitments into consideration when they schedule their dates.
Thank you, Delmobile!