I am surprised you are finding such a big difference between the cost of a round trip ticket to Rome and the cost of an open jaw ticket into Barcelona and out of Rome. I don't know where you're flying from, but I just plugged your dates into www.kayak.com from Boston, and the price was almost identical for round trip or open jaw.

Can you share where you're flying from and where you found the big disparity in fares?

Either way, though, you can fly between Barcelona and Rome on Vueling for 20 or 30 euro apiece one way, including all taxes. Some flights on some days are more expensive, you can plan around them. www.vueling.com