In this particular example (“the job had her
flying all over the country”) I'd suggest simply “přičemž”.
Here's a similar example:
Federica Mogheriniová se jakožto italská ministryně zahraničních věcí
v tomto obtížném a náročném období na mezinárodní scéně účastnila
dění v první linii, přičemž cestovala po
celém světě. (zdroj)
As (the) Italian Minister of Foreign Affairs in this difficult and
challenging time in international affairs, FM was in the thick of the
action,
- which had her travel all over the world.
- which had her travelling all over the
world.
- which saw her travel all over the world.
- which saw her travelling all over the
world.