I think it's pretty clear that you can't have visitors visiting both governments on the same visit. Simple diplomatic courtesy dictates separate (though equal) visits to both parties. A respectable interlude between visit would be, in my opinon, about three hours. This would provide ample time for one visit to be concluded, and a full transition to the next visit. It's simple logic really...
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U.S., allies conduct 22 strikes against ISIS targets in Iraq, Syria (Reuters)
from the article: Israel to snub foreign envoys who meet with Hamas ministers