Are emotions local or purely global? Can there be two inconsistent emotions in different parts of the brain?
There are two assumptions in this question it may be useful to make explicit. First, there's an assumption that words like "emotion" or "motivation" have meaning at different levels of analysis like organs, neurons, atoms, etc. If when we say emotion we mean the subjective experience, it's not at all clear that meaning exists at the neuronal level. This is related to a grand paradox (below), but even if we backed off from that, connecting subjective with objective creates thorny problems.


  https://en.wikipedia.org/wiki/Hard_problem_of_consciousness


Second, the question sort of implies that cognitive functions are carried out by limited areas. This is looking less and less true; there is some evidence for specialized functions, but in general most complex operations (including emotion) are influenced from a complex forward-and-backward activation-and-inhibition cascades in multiple areas.


  https://en.wikipedia.org/wiki/Functional_specialization_(brain)


The experience of emotions appear caused by / related to / influenced by complex cascades of activity across the brain. It's not clear that the words we use to describe the feelings map onto such neuronal activation/inhibition patterns, but even if they did, there's no reason to assume that such patterns of neuronal activation wouldn't co-occur.

tl;dr: Yes.