Hi Colin, I am not aware of the rules regarding taking animals on trains and buses, as I have no animals.
My wife is allergic to cats, dogs and other domestic animals, so clearly, we have never had this situation.
However, we have travelled by train into Valencia, which are excellent. Clean, punctual and they are very good value for money.
I have had a quick look on the Renfe train site and you could ask the question online, where a virtual assistant should help you.
Having quickly visited the site, I found that they do allow dogs up to 10 kilos in weight subject to certain conditions.
As for buses and taxis, I do not know.
Regarding taking your dogs onto beaches, as xetog has stated, in the Valencian Province, dogs are allowed on beaches at certain times of the year. Hope this helps.