I just got back from Abu Dhabi - from the US, you won't be hassled at all at immigration. UAE wants visitors to come in and spend money - Americans fit that description. You arriving in AUH and departing DXB means you'll spend some money.

In the 200+ trips through immigration all around the world over the past 30 years, I've never been asked to show a departing ticket. The most I've ever traveled with is a print out of an itinerary, but in some cases did not even have that as I was departing by car or ferry or train or had not yet decided.