I looked at traveling through Alicante on the way to Valencia.
There was very little flight flexibility, and the trains from Valencia started late on the Sunday, although an overnight stop might have been fun. Minutes after booking a trip via Barcelona, I had the http://www.flybe.com site pointed out there are three flights a day to Alicante. Maybe next time.
What I originally wrote
How much and how frequent are the trains from Alicante to Valencia? When are the flights? How long’s the journey?
The Renfe site is great. Between 90 mins, and 2 hours, price varies with c. €27.50 for the express and €12.50 for the Regional line. About once/hour.
View Valencia in a larger map
BA don’t have that many scheduled flights to Alicante. They fly from LGW and are only offering a 06:25 AM flight. This looks like a no-no. Even with stops on the way. I calculate an 8.5 hour journey.