We need to find the easiest way to get from amalfi to either split or Dubrovnik! What would you suggest?

Train to Bari, ferry to Dubrovnik. Train to Pescara or Ancona, ferry to Split.

http://www.visit-croatia.co.uk/gettingthere/ferry.htm

The easiest is to train to Bari, Italy & ferry to Dubrovnik. Here's a link to Croatia's ferry line map. I did the overnight ferry from Ancona to Split. The ferry line is by no means luxurious. But, the Croatians are very kind and very willing to please. The ferry was packed on my way to Croatia in August & virtually empty on my return in September. Depending on the time of year, reservations may be necessary. I booked mine prior to leaving home.
http://www.jadrolinija.hr/default.aspx?dpid=1227

Summer 2010 we did that combo. We trained to Rome and flew Easyjet to Dubrovnik (and back to Rome from Split). But we didn't mind having a few days in Rome, in fact we wanted it. The flights were obscenely cheap, I think 14€.