Why would a passenger plane arrive so close to the President's plane? Not sure how things work there, but it would be prudent for ATC to hold regular arrivals and takeoffs for a block of time.
Under normal circumstance, go arounds are quite normal. On a recent CX flight arriving in JFK, the pilot decided to perform a go around because the perceding arrival plane was taking too long pulling out of an active runway. Even more recently, I was on an HX flight which incurred not one but two go arounds due to wind shear at PEK. We diverted to TSN. No one clapped on either flight, pretty normal stuff IMO.