I agree, it is not easy getting into or out of Croatia by plane, but are you flying into Dubrovnik and out of Split? And to where?

When you are checking flights out of Split, some are not every day. So maybe it is better to check with a travel agent in that case - they have a lot more info at their fingertips.

I think I will do that Rialto, thank you everyone!

I'm working on a trip to Croatia/Italy now. From DFW you can fly direct to Frankfurt and then take either the Croatian airline or several others (see Kayak.com) to get to Dubrovnik or Split. I am going on miles to FRA and then buying my own ticket to Croatia. I could have used miles all of the way but did not want all day or night layovers. There is a direct flight on the Croatian airline from FRA to Dubrovnik.
I think it's sometimes less expensive to break up the flights and buy separate tickets.
Another thought is the direct flight from DFW to Madrid. There is a non-stop flight from MAD to Dubrovnik. This might work out better for you since you want to visit family in Spain.