My family and I are traveling to Israel for the first time and want to hop over to Jordan to take in a few sights. I've read about Wadi Rum, Petra, Lot's cave, and Jerash. If we cross over at Eliat and return via the King's Bridge (?), will we have problems coming in that way? (We don't have visas and I've read you cannot get one at this crossing)
Additionally, we only speak English. Are there buses that run between these places and are we going to have a difficult time finding our way around? Is it safe? Are there other sights we should see? Any places to stay recommended?